QuestionBerechne die Höhe auf die Hypotenuse $c$ für die gegebenen Seitenlängen: a) $c=5 \mathrm{~cm}, a=3 \mathrm{~cm}, b=4 \mathrm{~cm}$ ; b) $c=25 \mathrm{~cm}, a=15 \mathrm{~cm}, b=20 \mathrm{~cm}$ .

Studdy Solution

STEP 1

Assumptions1. All measurements are in centimeters. . All triangles are right-angled.
3. For each triangle, the given sides and heights are perpendicular to each other.
4. The formula for the area of a triangle is $Area =0.5 \times base \times height$ .

STEP 2

For the first problem, we are given $c=7.2cm$ , $a=4cm$ , and $h_c=.5cm$ . We need to find $h_a$ . We can use the formula for the area of a triangle to solve this.
$Area =0.5 \times a \times h_a =0.5 \times c \times h_c$

STEP 3

Substitute the given values into the equation.
$0.5 \times \times h_a =0.5 \times7.2 \times3.5$

STEP 4

olve for $h_a$ .
$h_a = \frac{0. \times7.2 \times3.}{0. \times4} =6.3cm$

STEP 5

For the second problem, we are given $a=9.cm$ , $b=4cm$ , and $h_a=5.5cm$ . We need to find $h_b$ . We can use the formula for the area of a triangle to solve this.
$Area =0.5 \times a \times h_a =0.5 \times b \times h_b$

STEP 6

Substitute the given values into the equation.
$0.5 \times9.6 \times5.5 =0.5 \times4 \times h_b$

STEP 7

olve for $h_b$ .
$h_b = \frac{0.5 \times9.6 \times5.5}{0.5 \times4} =13.2cm$

STEP 8

For the third problem, we are given $c=11.2cm$ , $h_c=7.7cm$ , and $h_b=5.6cm$ . We need to find $b$ . We can use the formula for the area of a triangle to solve this.
$Area =0.5 \times c \times h_c =0.5 \times b \times h_b$

STEP 9

Substitute the given values into the equation.
$.5 \times11.2 \times7.7 =.5 \times b \times5.6$

STEP 10

olve for $b$ .
$b = \frac{0.5 \times.2 \times7.7}{0.5 \times5.6} =15.68cm$

STEP 11

For the fourth problem, we are given $a=3cm$ , $b=4cm$ , and $c=5cm$ . We need to find $h_c$ . We can use the formula for the area of a triangle to solve this.
$Area =0.5 \times a \times b =0.5 \times c \times h_c$

STEP 12

Substitute the given values into the equation.
$0.5 \times \times4 =0.5 \times5 \times h_c$

STEP 13

olve for $h_c$ .
$h_c = \frac{0.5 \times3 \times}{0.5 \times5} =2.cm$

STEP 14

For the fifth problem, we are given $a=cm$ , $b=20cm$ , and $c=25cm$ . We need to find $h_c$ . We can use the formula for the area of a triangle to solve this.
$Area =0. \times a \times b =0. \times c \times h_c$

STEP 15

Substitute the given values into the equation.
$0.5 \times15 \times20 =0.5 \times25 \times h_c$

STEP 16

olve for $h_c$ .
$h_c = \frac{0.5 \times15 \times20}{0.5 \times25} =12cm$ The solutions are $h_a=6.3cm$ , $h_b=13.2cm$ , $b=15.68cm$ , $h_c=2.4cm$ for the fourth problem, and $h_c=12cm$ for the fifth problem.

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QuestionBerechne die Höhe auf die Hypotenuse $c$ für die gegebenen Seitenlängen: a) $c=5 \mathrm{~cm}, a=3 \mathrm{~cm}, b=4 \mathrm{~cm}$ ; b) $c=25 \mathrm{~cm}, a=15 \mathrm{~cm}, b=20 \mathrm{~cm}$ .

Studdy Solution

STEP 1

Assumptions1. All measurements are in centimeters. . All triangles are right-angled.
3. For each triangle, the given sides and heights are perpendicular to each other.
4. The formula for the area of a triangle is $Area =0.5 \times base \times height$ .

STEP 2

For the first problem, we are given $c=7.2cm$ , $a=4cm$ , and $h_c=.5cm$ . We need to find $h_a$ . We can use the formula for the area of a triangle to solve this.
$Area =0.5 \times a \times h_a =0.5 \times c \times h_c$

STEP 3

Substitute the given values into the equation.
$0.5 \times \times h_a =0.5 \times7.2 \times3.5$

STEP 4

olve for $h_a$ .
$h_a = \frac{0. \times7.2 \times3.}{0. \times4} =6.3cm$

STEP 5

For the second problem, we are given $a=9.cm$ , $b=4cm$ , and $h_a=5.5cm$ . We need to find $h_b$ . We can use the formula for the area of a triangle to solve this.
$Area =0.5 \times a \times h_a =0.5 \times b \times h_b$

STEP 6

Substitute the given values into the equation.
$0.5 \times9.6 \times5.5 =0.5 \times4 \times h_b$

STEP 7

olve for $h_b$ .
$h_b = \frac{0.5 \times9.6 \times5.5}{0.5 \times4} =13.2cm$

STEP 8

For the third problem, we are given $c=11.2cm$ , $h_c=7.7cm$ , and $h_b=5.6cm$ . We need to find $b$ . We can use the formula for the area of a triangle to solve this.
$Area =0.5 \times c \times h_c =0.5 \times b \times h_b$

STEP 9

Substitute the given values into the equation.
$.5 \times11.2 \times7.7 =.5 \times b \times5.6$

STEP 10

olve for $b$ .
$b = \frac{0.5 \times.2 \times7.7}{0.5 \times5.6} =15.68cm$

STEP 11

For the fourth problem, we are given $a=3cm$ , $b=4cm$ , and $c=5cm$ . We need to find $h_c$ . We can use the formula for the area of a triangle to solve this.
$Area =0.5 \times a \times b =0.5 \times c \times h_c$

STEP 12

Substitute the given values into the equation.
$0.5 \times \times4 =0.5 \times5 \times h_c$

STEP 13

olve for $h_c$ .
$h_c = \frac{0.5 \times3 \times}{0.5 \times5} =2.cm$

STEP 14

For the fifth problem, we are given $a=cm$ , $b=20cm$ , and $c=25cm$ . We need to find $h_c$ . We can use the formula for the area of a triangle to solve this.
$Area =0. \times a \times b =0. \times c \times h_c$

STEP 15

Substitute the given values into the equation.
$0.5 \times15 \times20 =0.5 \times25 \times h_c$

STEP 16

olve for $h_c$ .
$h_c = \frac{0.5 \times15 \times20}{0.5 \times25} =12cm$ The solutions are $h_a=6.3cm$ , $h_b=13.2cm$ , $b=15.68cm$ , $h_c=2.4cm$ for the fourth problem, and $h_c=12cm$ for the fifth problem.

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QuestionBerechne die Höhe auf die Hypotenuse ccc für die gegebenen Seitenlängen: a) c=5 cm,a=3 cm,b=4 cmc=5 \mathrm{~cm}, a=3 \mathrm{~cm}, b=4 \mathrm{~cm}c=5 cm,a=3 cm,b=4 cm; b) c=25 cm,a=15 cm,b=20 cmc=25 \mathrm{~cm}, a=15 \mathrm{~cm}, b=20 \mathrm{~cm}c=25 cm,a=15 cm,b=20 cm.

Studdy Solution

STEP 1

Assumptions1. All measurements are in centimeters. . All triangles are right-angled.3. For each triangle, the given sides and heights are perpendicular to each other.4. The formula for the area of a triangle is Area=0.5×base×heightArea =0.5 \times base \times heightArea=0.5×base×height.

STEP 2

STEP 3

Substitute the given values into the equation.0.5××ha=0.5×7.2×3.50.5 \times \times h_a =0.5 \times7.2 \times3.50.5××ha​=0.5×7.2×3.5

STEP 4

olve for hah_aha​.ha=0.×7.2×3.0.×4=6.3cmh_a = \frac{0. \times7.2 \times3.}{0. \times4} =6.3cmha​=0.×40.×7.2×3.​=6.3cm

STEP 5

STEP 6

Substitute the given values into the equation.0.5×9.6×5.5=0.5×4×hb0.5 \times9.6 \times5.5 =0.5 \times4 \times h_b0.5×9.6×5.5=0.5×4×hb​

STEP 7

olve for hbh_bhb​.hb=0.5×9.6×5.50.5×4=13.2cmh_b = \frac{0.5 \times9.6 \times5.5}{0.5 \times4} =13.2cmhb​=0.5×40.5×9.6×5.5​=13.2cm

STEP 8

STEP 9

Substitute the given values into the equation..5×11.2×7.7=.5×b×5.6.5 \times11.2 \times7.7 =.5 \times b \times5.6.5×11.2×7.7=.5×b×5.6

STEP 10

olve for bbb.b=0.5×.2×7.70.5×5.6=15.68cmb = \frac{0.5 \times.2 \times7.7}{0.5 \times5.6} =15.68cmb=0.5×5.60.5×.2×7.7​=15.68cm

STEP 11

For the fourth problem, we are given a=3cma=3cma=3cm, b=4cmb=4cmb=4cm, and c=5cmc=5cmc=5cm. We need to find hch_chc​. We can use the formula for the area of a triangle to solve this.Area=0.5×a×b=0.5×c×hcArea =0.5 \times a \times b =0.5 \times c \times h_cArea=0.5×a×b=0.5×c×hc​

STEP 12

Substitute the given values into the equation.0.5××4=0.5×5×hc0.5 \times \times4 =0.5 \times5 \times h_c0.5××4=0.5×5×hc​

STEP 13

olve for hch_chc​.hc=0.5×3×0.5×5=2.cmh_c = \frac{0.5 \times3 \times}{0.5 \times5} =2.cmhc​=0.5×50.5×3×​=2.cm

STEP 14

For the fifth problem, we are given a=cma=cma=cm, b=20cmb=20cmb=20cm, and c=25cmc=25cmc=25cm. We need to find hch_chc​. We can use the formula for the area of a triangle to solve this.Area=0.×a×b=0.×c×hcArea =0. \times a \times b =0. \times c \times h_cArea=0.×a×b=0.×c×hc​

STEP 15

Substitute the given values into the equation.0.5×15×20=0.5×25×hc0.5 \times15 \times20 =0.5 \times25 \times h_c0.5×15×20=0.5×25×hc​

STEP 16

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QuestionBerechne die Höhe auf die Hypotenuse $c$ für die gegebenen Seitenlängen: a) $c=5 \mathrm{~cm}, a=3 \mathrm{~cm}, b=4 \mathrm{~cm}$ ; b) $c=25 \mathrm{~cm}, a=15 \mathrm{~cm}, b=20 \mathrm{~cm}$ .

Assumptions1. All measurements are in centimeters. . All triangles are right-angled.
3. For each triangle, the given sides and heights are perpendicular to each other.
4. The formula for the area of a triangle is $Area =0.5 \times base \times height$ .

Substitute the given values into the equation.
$0.5 \times \times h_a =0.5 \times7.2 \times3.5$

olve for $h_a$ .
$h_a = \frac{0. \times7.2 \times3.}{0. \times4} =6.3cm$

Substitute the given values into the equation.
$0.5 \times9.6 \times5.5 =0.5 \times4 \times h_b$

olve for $h_b$ .
$h_b = \frac{0.5 \times9.6 \times5.5}{0.5 \times4} =13.2cm$

Substitute the given values into the equation.
$.5 \times11.2 \times7.7 =.5 \times b \times5.6$

olve for $b$ .
$b = \frac{0.5 \times.2 \times7.7}{0.5 \times5.6} =15.68cm$

For the fourth problem, we are given $a=3cm$ , $b=4cm$ , and $c=5cm$ . We need to find $h_c$ . We can use the formula for the area of a triangle to solve this.
$Area =0.5 \times a \times b =0.5 \times c \times h_c$

Substitute the given values into the equation.
$0.5 \times \times4 =0.5 \times5 \times h_c$

olve for $h_c$ .
$h_c = \frac{0.5 \times3 \times}{0.5 \times5} =2.cm$

For the fifth problem, we are given $a=cm$ , $b=20cm$ , and $c=25cm$ . We need to find $h_c$ . We can use the formula for the area of a triangle to solve this.
$Area =0. \times a \times b =0. \times c \times h_c$

Substitute the given values into the equation.
$0.5 \times15 \times20 =0.5 \times25 \times h_c$