# Math Help - Trigonometry Word Problem ... Question 4

1. ## Trigonometry Word Problem ... Question 4

The following questions are for a final class project. Obviously these questions are very hard, and I am unsure how to completely answer these with the proper and complete work shown. Help on answering these questions with work/ steps would be greatly appreciated.

11. A round clock displays the time 2:30am. The length of the minute hand measures 18cm and the length of the hour hand measures 12cm. How far apart are the tips of the hands?

12. A group of mountain climbers are using trigonometry to find the height of a mountain. From point A which is due west of the mountain, the angle of elevation to the top is 27°. From point B which is due west of the mountain the angle is 34°. Point A and B are 9.5m apart. How high is the mountain?

11. A round clock displays the time 2:30am. The length of the minute hand measures 18cm and the length of the hour hand measures 12cm. How far apart are the tips of the hands?
The angle between the hands would be 105 degrees. (Can you see why?) And you know two sides of the triangle. Use the Law of Cosines to find the third side:

\begin{aligned}
c^2 &= a^2 + b^2 - 2ab\cos C \\
c^2 &= 12^2 + 18^2 - 2(12)(18)\cos 105^\circ \\
c^2 &\approx 144 + 324 + 111.81 \\
c^2 &\approx 144 + 324 + 111.81 \\
c^2 &\approx 579.81 \\
c &\approx 24.08
\end{aligned}

The hands are about 24.08cm apart.

01

3. Tyvm for the help here.

"The angle between the hands would be 105 degrees. (Can you see why?)"

Yes.

3.5 / 12 = B / 360
.........
105 = B

4. "12. A group of mountain climbers are using trigonometry to find the height of a mountain. From point A which is due west of the mountain, the angle of elevation to the top is 27°. From point B which is due west of the mountain the angle is 34°. Point A and B are 9.5m apart. How high is the mountain?"

Both points are west of the mountain. How do I even draw a diagram to show this?

5. Edit:

I attempted a diagram to display the situation. Is this correct so far?

6. Or is the 34 degrees supposed to be like this?

7. Theta = 180° - 34°
Theta = 146°

Angle C = 180° - 27° - 146°
Angle C = 7°

Sin A / a = Sin C / c
Sin 27° / a = Sin 7° / 9.5
(Cross Multiplication...)
13.8m = a

Sin B = O / H
Sin 34° = b / 13.8
(Cross Multiplication...)
7.3m = b

Therefore the mountain is 7.3m tall.

Is this the right answer? (I really hope so!)