Question

A hiker walks along a path and comes to a cliff. He wants to find out how high the cliff is, so he ties a 110 foot cable to a rock at the top, and tosses the rest of the cable over the cliff. When the hiker gets to the bottom, he pulls the cable to length, and measures the angle that it makes with the ground. What function will he use to determine the height of the cliff, and what is the height if the angle is 25º?

Answer 1

B. sine; 46.5 feet high

Explanation:

In this case, we use trigonometric ratio.

Assuming the horizontal ground, the cable and the height of the cliff forms a triangle,

The cable is the hypotenuse, the height of the cliff is opposite to the angle formed by the cable and the horizontal ground.

Thus; the most appropriate function is sine

Such that;

Sine θ = Opposite/Hypotenuse

Where; θ = 25°, opposite is the height of the cliff and hypotenuse is the cable, 110 ft

Therefore;

Sine 25° = Opp/ 110

Hence;

Opp = 110 ft × sine 25°

= 46.488 ft

= 46.5 ft

Therefore;

The function is Sine, and the height of the cliff is 46.5 ft high