3D Triginometry Question (1 Viewer)

[cowanny]

Please I need help with this question:
Tylah and Jacob are on level ground 200m apart. A building is due north of Tylah and on a bearing of 75 degrees true from Jacob. The top of the building appears at an angle of elevation of 24 degrees to Tylah and 16 degrees to Jacob. Find the height of the building?
Please post full working
Thanks

 

[Ikki]

LOL sorry but I can't draw a diagram on this but you should be able to follow my steps.

Denoting the points with the initials of the person I drew a flat triangle with Jacob on left, Tylah on the right and the building up north.
By using trig on the 3D diagram (you can draw and h is the height of the building) JB=hcot16 and TB=hcot24.
JT is 200. The bearing true is 75 degrees from Jacob to the building. If you draw in compass guidelines for each points you see angle JBT is alternate angle to that bearing. Therefore, Angle JNT=75 degrees.

Now use cosine rule and rearrange for h^2 and then square root to find the final answer.