Questions: A plane rises from take-off and flies at an angle of 5° with the horizontal runway. When it has gained 600 feet, find the distance, to the nearest foot, the plane has flown. An angle θ and the opposite leg of a right triangle are given. Identify the trigonometric function that can be used to find the hypotenuse. A. tangent B. sine C. cosine

A plane rises from take-off and flies at an angle of 5° with the horizontal runway. When it has gained 600 feet, find the distance, to the nearest foot, the plane has flown.

An angle θ and the opposite leg of a right triangle are given. Identify the trigonometric function that can be used to find the hypotenuse.
A. tangent
B. sine
C. cosine

Transcript text: A plane rises from take-off and flies at an angle of $5^{\circ}$ with the horizontal runway. When it has gained 600 feet, find the distance, to the nearest foot, the plane has flown. An angle $\theta$ and the opposite leg of a right triangle are given. Identify the trigonometric function that can be used to find the hypotenuse. A. tangent B. sine C. cosine

Solution

Solution Steps

Step 1: Identify the given information

We are given the angle of elevation, 5°, and the opposite side (altitude gained), 600 ft. We need to find the hypotenuse, which represents the distance the plane has flown.

Step 2: Choose the correct trigonometric function

We have the angle and the opposite side, and we want to find the hypotenuse. The trigonometric function that relates these three is sine:

sin(angle) = opposite / hypotenuse

Step 3: Set up the equation and solve for the hypotenuse

sin(5°) = 600 ft / hypotenuse

hypotenuse = 600 ft / sin(5°)

hypotenuse ≈ 600 ft / 0.08716

hypotenuse ≈ 6888.28 ft

Step 4: Round to the nearest foot

hypotenuse ≈ 6888 ft