Trigonometry: Wanting someone to check my answer for Statics

[blixel]

Homework Statement

A building is 400 ft tall and has suffered damage from a recent earthquake. If a surveyor is stationed 150 ft away, sets a zero angle on the bottom corner of the building, and turns the angle shown to the top of the building; what is the angle at which the building is leaning with respect to vertical?

Homework Equations

I feel like I know what to do, but would like confirmation from the forum please.

The Attempt at a Solution

sin(70)/400 = sinC/150
sinC=[150*sin(70)]/400
C=arcsin([150*sin(70)]/400)~=20.6332
180-70-20.6332=89.3668

Therefore, Beta = 89.3668

 

[gneill]

Your work looks fine to me

 

[Delta2]

Seems correct to me. You use sine law to determine sinC and therefore C (provided that $C<90$), and then knowing C and the angle of 70 degrees can determine the other angle of the triangle.

Just to add something if angle beta was smaller or the building height was not so big, angle C might have been >90 degrees.

 

[blixel]

Your work looks fine to me

Thanks for checking it over. The work felt right, but the image suggests a steeper angle, so I wasn't confident.