Answer:
<em>HT </em>= 17
<<em>T</em> = 62°
<<em>H</em> = 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 <<em>T</em>. Since we know the measure of two sides, opposite (15) and adjacent (8), use the formula for tangent as tangent is opposite/adjacent.
Tangent = =
= 1.875
Use the tan⁻¹ button on the calculator to find the value for <<em>T.</em>
tan⁻¹(1.875) = 61.9°
<<em>T = </em>62°
3. To find the measure of <<em>H, </em>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 = =
= 0.5333333333
Take the tan⁻¹ to get the measure of <<em>H.</em>
tan⁻¹(0.5333333333) = 28.07 = 28°
Hope this helps. Please give a thanks and mark as brainliest. :)