QuestionFind the distance from a rock to a tree, given a stake 24.0 yards north of the rock with a bearing of $S 16.0^{\circ} W$ . Round to the nearest tenth of a yard.

Studdy Solution

STEP 1

Assumptions1. The tree is due west of the rock. . The stake is24.0 yards north of the rock.
3. The bearing of the tree from the stake is16.0° W.
4. We're asked to find the distance from the rock to the tree.

STEP 2

We can solve this problem using trigonometry. The situation described forms a right triangle where the stake is one vertex, the rock is another vertex, and the tree is the third vertex. The angle at the stake is16.0°.

STEP 3

The distance from the rock to the tree (which we'll call "d") can be found using the tangent of the angle at the stake. The tangent of an angle in a right triangle is the ratio of the side opposite the angle to the side adjacent to the angle. In this case, the side opposite the angle is the distance from the stake to the tree (which we'll call "a") and the side adjacent to the angle is the distance from the rock to the stake (which is24.0 yards).
$tan(16.0°) = \frac{a}{24.0\, yards}$

STEP 4

We can solve this equation for "a" to find the distance from the stake to the tree.
$a =24.0\, yards \times tan(16.0°)$

STEP 5

Calculate the distance from the stake to the tree.
$a =24.0\, yards \times tan(16.0°) \approx.9\, yards$

STEP 6

Now we can find the distance from the rock to the tree. This is the hypotenuse of the right triangle, so we can use the Pythagorean theorem to find it.
$d = \sqrt{(24.0\, yards)^2 + (6.9\, yards)^2}$

STEP 7

Calculate the distance from the rock to the tree.
$d = \sqrt{(24.0\, yards)^2 + (6.9\, yards)^2} \approx25.0\, yards$ The distance from the rock to the tree is approximately25.0 yards.

Was this helpful?

QuestionFind the distance from a rock to a tree, given a stake 24.0 yards north of the rock with a bearing of $S 16.0^{\circ} W$ . Round to the nearest tenth of a yard.

Studdy Solution

STEP 1

Assumptions1. The tree is due west of the rock. . The stake is24.0 yards north of the rock.
3. The bearing of the tree from the stake is16.0° W.
4. We're asked to find the distance from the rock to the tree.

STEP 2

We can solve this problem using trigonometry. The situation described forms a right triangle where the stake is one vertex, the rock is another vertex, and the tree is the third vertex. The angle at the stake is16.0°.

STEP 3

STEP 4

We can solve this equation for "a" to find the distance from the stake to the tree.
$a =24.0\, yards \times tan(16.0°)$

STEP 5

Calculate the distance from the stake to the tree.
$a =24.0\, yards \times tan(16.0°) \approx.9\, yards$

STEP 6

Now we can find the distance from the rock to the tree. This is the hypotenuse of the right triangle, so we can use the Pythagorean theorem to find it.
$d = \sqrt{(24.0\, yards)^2 + (6.9\, yards)^2}$

STEP 7

Calculate the distance from the rock to the tree.
$d = \sqrt{(24.0\, yards)^2 + (6.9\, yards)^2} \approx25.0\, yards$ The distance from the rock to the tree is approximately25.0 yards.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the distance from a rock to a tree, given a stake 24.0 yards north of the rock with a bearing of S16.0∘WS 16.0^{\circ} WS16.0∘W. Round to the nearest tenth of a yard.

Studdy Solution

STEP 1

Assumptions1. The tree is due west of the rock. . The stake is24.0 yards north of the rock.3. The bearing of the tree from the stake is16.0° W.4. We're asked to find the distance from the rock to the tree.

STEP 2

We can solve this problem using trigonometry. The situation described forms a right triangle where the stake is one vertex, the rock is another vertex, and the tree is the third vertex. The angle at the stake is16.0°.

STEP 3

STEP 4

We can solve this equation for "a" to find the distance from the stake to the tree.a=24.0 yards×tan(16.0°)a =24.0\, yards \times tan(16.0°)a=24.0yards×tan(16.0°)

STEP 5

Calculate the distance from the stake to the tree.a=24.0 yards×tan(16.0°)≈.9 yardsa =24.0\, yards \times tan(16.0°) \approx.9\, yardsa=24.0yards×tan(16.0°)≈.9yards

STEP 6

Now we can find the distance from the rock to the tree. This is the hypotenuse of the right triangle, so we can use the Pythagorean theorem to find it.d=(24.0 yards)2+(6.9 yards)2d = \sqrt{(24.0\, yards)^2 + (6.9\, yards)^2}d=(24.0yards)2+(6.9yards)2​

STEP 7

Calculate the distance from the rock to the tree.d=(24.0 yards)2+(6.9 yards)2≈25.0 yardsd = \sqrt{(24.0\, yards)^2 + (6.9\, yards)^2} \approx25.0\, yardsd=(24.0yards)2+(6.9yards)2​≈25.0yardsThe distance from the rock to the tree is approximately25.0 yards.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the distance from a rock to a tree, given a stake 24.0 yards north of the rock with a bearing of $S 16.0^{\circ} W$ . Round to the nearest tenth of a yard.

Assumptions1. The tree is due west of the rock. . The stake is24.0 yards north of the rock.
3. The bearing of the tree from the stake is16.0° W.
4. We're asked to find the distance from the rock to the tree.

We can solve this equation for "a" to find the distance from the stake to the tree.
$a =24.0\, yards \times tan(16.0°)$

Calculate the distance from the stake to the tree.
$a =24.0\, yards \times tan(16.0°) \approx.9\, yards$

Now we can find the distance from the rock to the tree. This is the hypotenuse of the right triangle, so we can use the Pythagorean theorem to find it.
$d = \sqrt{(24.0\, yards)^2 + (6.9\, yards)^2}$

Calculate the distance from the rock to the tree.
$d = \sqrt{(24.0\, yards)^2 + (6.9\, yards)^2} \approx25.0\, yards$ The distance from the rock to the tree is approximately25.0 yards.