Answer this trig ques on height and dist?

Let height of the temple be H ...when solved H=150 meters

Clarifying the positions: I am not able to create a diagram, but I will 'verbalize' one.

Draw a circle and place a dot (mark this as A) at its center. place 4 dots, each equidistant around the circumference, thus they are 90 degrees apart, label the 4 dots, in a clockwise direction,(start anywhere) as N(north), next E(east), next S(south, next W(west). This represent the directional orientation to the temple A (center dot) Now place a "P" at dot E(east), and place "Q" at dot S(south)

NOTE: the angle between AP and AQ is 90 degrees.......AP and AQ are the two sides to a right triangle that is formed on the ground with a hypotenuse of PQ= 100 sq. rt3

Solving the problem: the distance to the south (AQ), where the elevation is 45* is =H (tan 45*)

.....AQ=H( tan45*)=H

the distance to the east (AP), where the elavation is 60* is =H (tan 60*)

......AP=H(tan 60*)= H/ (sq. rt 3)

Solve for H...temple's height ..................note: sq. rt 3=1.732

the ground right triangle has sides of H meters, H/ (sq.rt 3) meters, and a hypotenuse of 100(sq.rt3)

..........squaring the sides and sum up: H^2 + (H/sq.rt3)^2= (100 sq.rt3)^2

4 H^2=10000(9) H^2=2500(9) H=50(3)=150

surely if I further them as a sprint this is bc i for my section savor their q's and their a's so i'm going to probable shop answering them in spite of the fact that if i are not getting BA. besides the incontrovertible fact that this is an further bonus.

No diagram, no drawing

I find that :

2h² +(100√3)² = h² (1/(sin60)² + 1/(sin45)²)

you simplify and you get h : the height

h =150m