Ryan \( (\mathrm{R}) \) is looking up at the cliff of a mountain. He is 50 m from B. the bottom of mountain and the angle of elevation from where he stands is \( 66^{\circ} \) Determine the perpendicular height of the mountain. (Use question 4 as a guideline. The diagram is not drawn according to scale)

To determine the perpendicular height of the mountain, we can use the tangent of the angle of elevation. The relationship can be expressed as: \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \] In this case, \(\theta = 66^{\circ}\), the opposite side is the height of the mountain (let's call it \(h\)), and the adjacent side is the distance from Ryan to the base of the mountain, which is 50 m. Thus, we have: \[ \tan(66^{\circ}) = \frac{h}{50} \] Now, rearranging the formula to solve for \(h\): \[ h = 50 \cdot \tan(66^{\circ}) \] Calculating this with a calculator: \[ h \approx 50 \cdot 2.246 = 112.3 \, \text{m} \] So, the perpendicular height of the mountain is approximately \(112.3\) meters.