Question

Solve the right triangle ABC, where C = 90°.

a = 75.4 yd, b=41.7 yd
=yd
(Simplify your answer. Type an integer or a decimal. Round to the nearest tenth as needed.)
C=
A='0'
(Simplify your answers. Type integers. Round to the nearest ten minutes as needed.)
B='0'
(Simplify your answers. Type integers. Round to the nearest ten minutes as needed.)

Answer 1

Answer: We can use the Pythagorean theorem to find the length of the hypotenuse (c) of the triangle:

c = √(a^2 + b^2) = √(75.4^2 + 41.7^2) = √(5702.76 + 1738.69) = √(7441.45)

c ≈ 86.38 yd

Next, we can use the inverse cosine function (arccos) to find angle A:

A = arccos(a/c) = arccos(75.4/86.38)

A ≈ 30.49°

Finally, we can use the complementary angle formula to find angle B:

B = 90° - A

B ≈ 59.51°

So, the length of the hypotenuse is approximately 86.38 yards, angle A is approximately 30.49 degrees, and angle B is approximately 59.51 degrees.

Explanation: