Question

You want to visit your friend, John, at his house. You leave your house and walk down Oak Street which is at an angle 45◦ from Elm Street which is the street in front of your house. After walking 6 blocks, you arrive at John’s house. How far is Oak Street from Elm Street? Round to the nearest tenth of a block.

Use SOH CAH TOA to find d.

Answer 1

4.2 blocks

Explanation:

Reference angle (θ) = 45°

Opposite side to θ = d

Hypotenuse = 6

Using SOHCAHTOA, we would apply SOH since the Hypotenuse and Opposite side is what we are concerned with.

Thus:

Sin θ = Opp/Hyp

Substitute

Sin 45° = d/6

Multiply both sides by 6

6 × Sin 45 = d

d = 4.24264069

d = 4.2 (nearest tenth)

Therefore, the distance of Oak Street from Elm Street = 4.2 blocks