Question

Can someone help please

Answer 1

Answer:

HT = 17

<T = 62°

<H = 28°

Step-by-step explanation:

1. Use the Pythagorean Theorem to find the length of the missing side.

a² + b² = c²

15² + 8² = c²

225 + 64 = c²

289 = c²

√289 = c

c = 17

The length of side HT is 17.

2. Use SOHCAHTOA to find the measure of <T. Since we know the measure of two sides, opposite (15) and adjacent (8), use the formula for tangent as tangent is opposite/adjacent.

Tangent = $\frac{opposite}{adjacent}$  = $\frac{15}{8}$ = 1.875

Use the tan⁻¹ button on the calculator to find the value for <T.

tan⁻¹(1.875) = 61.9°

<T = 62°

3. To find the measure of <H, you can either add up the two angles and subtract from 180° or use SOHCAHTOA.

90° + 61.9° + x = 180°

151.9° + x = 180°

x = 28°

or

We know two sides: opposite (8) and adjacent (15). So, we will use tangent.

Tangent = $\frac{opposite}{adjacent}$ =  $\frac{8}{15}$ = 0.5333333333

Take the tan⁻¹ to get the measure of <H.

tan⁻¹(0.5333333333) = 28.07 = 28°

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