Math  /  Trigonometry

QuestionIf the opposite side of a triangle is 12.4 units long, and the hypotenuse is 67.8 units long, what is the length of the side adjacent? (A) 66.54 units (B) 66.65 units (C) 66.66 units (D) 66.67 units

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. The length of the opposite side is 12.4 12.4 units.
3. The length of the hypotenuse is 67.8 67.8 units.
4. We need to find the length of the adjacent side.

STEP 2

1. Recall the Pythagorean theorem.
2. Rearrange the formula to solve for the adjacent side.
3. Substitute the given values.
4. Calculate the length of the adjacent side.

STEP 3

Recall the Pythagorean theorem:
c2=a2+b2 c^2 = a^2 + b^2
where c c is the hypotenuse, a a is the opposite side, and b b is the adjacent side.

STEP 4

Rearrange the formula to solve for the adjacent side b b :
b2=c2a2 b^2 = c^2 - a^2

STEP 5

Substitute the given values into the formula:
b2=67.8212.42 b^2 = 67.8^2 - 12.4^2

STEP 6

Calculate the squares and the difference:
b2=4598.44153.76 b^2 = 4598.44 - 153.76 b2=4444.68 b^2 = 4444.68
Take the square root to find b b :
b=4444.68 b = \sqrt{4444.68} b66.67 b \approx 66.67
The length of the side adjacent is approximately:
66.67 units \boxed{66.67 \text{ units}}

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord