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)