Question

Suppose a right triangle has leg length b = 425.2 and the measure of angle B is 23. Which of these answers is closest to the lengths of the hypotenuse c and leg a?

1. Hypotenuse (c) ≈ 899.1
Leg (a) ≈ 399.1

2. Hypotenuse (c) ≈ 600.0
Leg (a) ≈ 350.0

3. Hypotenuse (c) ≈ 750.0
Leg (a) ≈ 400.0

4. Hypotenuse (c) ≈ 1000.0
Leg (a) ≈ 450.0

Answer 1

The length of the hypotenuse is approximately 899.1 and the length of the leg a is approximately 399.1.

Step-by-step explanation:

The length of the hypotenuse, c, can be found using the Pythagorean theorem, which states that a^2 + b^2 = c^2, where a and b are the lengths of the legs of the right triangle. In this case, the leg length b is given as 425.2 and the angle B is given as 23 degrees.

To find the length of the hypotenuse, use the formula c = sqrt(a^2 + b^2).

Substituting the given values, we have c = sqrt((425.2)^2 + (b)^2) = sqrt((425.2)^2 + (425.2)^2) ≈ 899.1.

The length of the leg a can be found using the formula a = b * tan(B), where B is the given angle. Substituting the values, we have a = 425.2 * tan(23) ≈ 399.1.