Question

In ΔHIJ, the measure of ∠J=90°, JI = 48, IH = 73, and HJ = 55. What is the value of the tangent of ∠H to the nearest hundredth?In ΔJKL, the measure of ∠L=90°, JL = 60, KJ = 61, and LK = 11. What ratio represents the tangent of ∠J?

Answer 1

11:60

Explanation:

In ΔHIJ, given the measure of ∠J=90°, JI = 48, IH = 73, and HJ = 55. We are to find tan<H

Using SOH CAH TOA

tan theta = opposite/adjacent

JI is the opposite (facing m<H)

HJ will be adjacent

tan m<H = JI/HJ

tan m<H = 48/55

tan m<H = 0.87 (to the nearest hundredth)

In ΔJKL, the measure of ∠L=90°, JL = 60, KJ = 61, and LK = 11. What ratio represents the tangent of ∠J?

Using SOH CAH TOA

tan theta = opposite/adjacent

LK is the opposite (facing m<J)

JL will be adjacent

tan m<J = LK/JL

tan m<H = 11/60

Hence the ratio that represents the tangent of ∠J is 11:60