Question

1. sue is on a lake in a boat 35 m away from the bottom of a cliff. when sue looks up at an angle of 40° she sees the top of the cliff. determine the height of the cliff.a=5t/i=5

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the adjacent side to the angle of elevation is 35 m and we want to find the opposite side (height of the cliff $h$). We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.
$\tan\theta=\frac{h}{35}$

Step2: Substitute the angle value

Given $\theta = 40^{\circ}$, we substitute it into the tangent formula:
$\tan40^{\circ}=\frac{h}{35}$
We know that $\tan40^{\circ}\approx0.8391$. So, $0.8391=\frac{h}{35}$

Step3: Solve for $h$

Multiply both sides of the equation by 35:
$h = 35\times\tan40^{\circ}$
$h=35\times0.8391\approx29.37$ m

Answer:

The height of the cliff is approximately 29.4 m.