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 = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{15}{8}[/tex] = 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 = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{8}{15}[/tex] = 0.5333333333
Take the tan⁻¹ to get the measure of <H.
tan⁻¹(0.5333333333) = 28.07 = 28°
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