Sally and Kate stand some distance away from a building which is 10m high. Sally measures the angle of elevation of the top of the building to be 35(degree). From Kate's position, the angle of elevation of the top of the building is 50(degree). If the angle SOK between Sally, Kate, and bottom of the building is 60(degree). Find

Question

Sally and Kate stand some distance away from a building which is 10m high. Sally measures the angle of elevation of the top of the building to be 35(degree). From Kate's position, the angle of elevation of the top of the building is 50(degree). If the angle SOK between Sally,  Kate, and bottom of the building is 60(degree). Find

A: the distance between Sally and Kate, correct to the nearest meter?
B: the angle SBK?

I tried finding the hypotenuse and solve but I get to a dead end. Any help is appreciated
Thanks Alot.

Steve · Answer

Apparently
O = base of building
B = top of building
If so, then

10/SO=tan35°
SO=14.28

10/KO=tan50°
KO=8.39
SK^2=SO^2+KO^2-2*SO*KO*cos60°=14.28^2+8.39^2-2*14.28*8.39*0.5=154.50
SK=12.43

Now use the same steps to find SB, KB, and angle SBK.