In right triangle PQD: tan47=h/y ---->h=ytan47 [1]
In right triangle PQE: tan36=h/x ---->h=xtan36 [2]
Equate [1] and [2]: ytan47=xtan36 ------->y=tan36x/tan47 [3]
In right triangle DQE: x^2+y^2=70^2
Substitute [3]: x^2+ (tan36x/tan47)^2= 4900 ---> x^2(tan^2(47)+tan^2(36))/tan^2(47))=4900
x= 70tan47/ sqr root:tan^2(47)+tan^2(36)
Substitute into [2]: h=tan36/tan47 * 50tan47/ sqr root:tan^2(47)+tan^2(36)
And the answer is 39.26304499 (I calculated it wrong the first time)
In right triangle PQE: tan36=h/x ---->h=xtan36 [2]
Equate [1] and [2]: ytan47=xtan36 ------->y=tan36x/tan47 [3]
In right triangle DQE: x^2+y^2=70^2
Substitute [3]: x^2+ (tan36x/tan47)^2= 4900 ---> x^2(tan^2(47)+tan^2(36))/tan^2(47))=4900
x= 70tan47/ sqr root:tan^2(47)+tan^2(36)
Substitute into [2]: h=tan36/tan47 * 50tan47/ sqr root:tan^2(47)+tan^2(36)
And the answer is 39.26304499 (I calculated it wrong the first time)