Question

to find width of river welevation of 61 deg. find d height of the tower n width of d rivet

Answer 1

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Let BC be the height of the tree,
AB be the breadth of the river

A be the initial position of the man
D be the final potion of the man

angle CAB =60°=60°
angle CDB =30°=30°

DA =40=40 m
Let AB = xx
Let BC = hh


Consider the triangle DBC
tan30=BCDB=BCDA+AB=h40+x 1√3=h40+xh=40+x√3⋯(1)tan⁡30=BCDB=BCDA+AB=h40+x 13=h40+xh=40+x3⋯(1)


Consider the triangle ABC
tan60=BCAB=hx √3=hxh=√3x⋯(2)tan⁡60=BCAB=hx 3=hxh=3x⋯(2)


Using (2) in (1)
h=40+x√3√3x=40+x√33x=40+x2x=40x=20