Chapter 8.2, Problem 40AYU

Finding the Height of a Mountain Use the illustration in Problem 37 to find the height QD of the mountain.

To determine

To find: The height of the mountain.

Answer to Problem 40AYU

Solution:

$620.9$ feet

Explanation of Solution

Given:

Height of the mountain

To find the length of the span of a proposed ski lift from $\text{P}$ to $\text{Q}$, a surveyor measures $\angle \text{DPQ}$ to be ${25}^{\circ }$ and then walks back a distance of 1000 feet to $\text{R}$ and measures $\angle \text{PRQ}$ to be ${15}^{\circ }$

Formula used:

$\frac{\text{sinA}}{\text{a}} = \frac{\text{sin}\text{B}}{\text{b}} = \frac{\text{sinC}}{\text{c}}$

$\angle \text{A} + \angle \text{B} + \angle \text{C} = {180}^{\circ }$

Calculation:

In the above figure angle $∟\text{QPD} = {25}^{\circ }$ and the angle eat $\text{D}$ is ${90}^0$ so the angle at $\text{Q}$ will be ${65}^0$ in the triangle $\text{QPD}$

And from the above solution we know that $\text{QP}$ value

So $\text{QP} = 1490.48$ feet

From the figure we clearly known that $\text{QP}$ is hypotenuse and $\text{QD}$ is opposite side so we can use sin angle to find the value of opposite side

So $\text{sin}{25}^{\circ } = \frac{\text{QD}}{\text{QP}} = \frac{\text{QD}}{1490.48}$

$\text{Sin}{25}^{\circ } \approx 0.42$

So $\text{QD} = \text{sin}25° \times 1490.48 \approx 629.90$feet

So the height of the mountain is $629.90$feet