Can someone help please

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 =  = = 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 = =   = 0.5333333333

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

tan⁻¹(0.5333333333) = 28.07 = 28°

Hope this helps. Please give a thanks and mark as brainliest. :)

11.33 feet.

Step-by-step explanation:

Given that the triangle is a right triangle ABC which has measure of angle ABC equal to 90 degrees and measure of angle ACB equal to 62 degrees.

The length of AB is 10 feet, which is opposite to angle ACB = 62 degrees.

The distance, in feet, that the box has to travel to move from point A to point C can be calculated by using trigonometry ratio. Since AC is the hypothenus of the triangle.

Using SinØ = opposite/hypothenus

That is

Sin Ø = AB / AC

Where Ø = 62 degree

Substitute Ø and length AB into the formula

Sin 62 = 10/ AC

AC = 10/ sin 62

AC = 10/ 0.8829

AC = 11. 33 feet.