Question

Solve the right triangle. Round your answers to the nearest tenth place.

Answer 1

for ac I got 11

ab i got 14

I'm not quite sure tho

but you could use SOH CAH TOA to find ab then use Pythagoras theorem to find AB

Answer 2

AB = 11.6 inches

AC = 7.3 inches

m∠B = 39°

Explanation:

To calculate side AB (c) put b (9 inches) over the sine of β (51°).

c = 9/sin(51)

The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse). This would be about 0.777.

c = 9/0.777

I recommend using a fraction here. 0.777 becomes 777/1000. Find the reciprocal (1000/777). Switch the sign to multiplication.

c = 9/1 * 1000/777

Cross cancel if needed.

c = 3/1 * 1000/259

Now multiply.

c = 3000/259

Divide 3000 by 259.

c ≈ 11.5830116 inches ≈ 11.6 inches

Now we know AB. To find AC, find the square root of AB² - BC².

AC = √(11.6² - 9²)

Square both 11.6 and 9.

AC = √(134.56 - 81)

Add 134.56 and 81 to get 53.56

AC = √53.56

Find the square root of 53.56

AC ≈ 7.31846979 ≈ 7.3 inches.

Finding the measure of angle B is comparatively simple. Subtract 51 from 90 to get 39° for angle B.