# FINDING AREA OF TRIANGLE WITH TRIGONOMETRY WORD PROBLEMS

Finding Area of Triangle with Trigonometry Word Problems :

Here we are going to see some example problems of finding area of triangle with trigonometry word problems.

## Finding Area of Triangle with Trigonometry Word Problems - Practice questions

Question 1 :

Find the area of a right triangle whose hypotenuse is 10 cm and one of the acute angle is 24° 24'

Solution : AC = Hypotenuse side = 10 cm

AB = Opposite side

Area of triangle  =  (1/2) ⋅ base ⋅ height

=  (1/2) ⋅ BC ⋅ AB

 sin θ  =  AB/ACsin 24° 24'  =  AB/100.4131 x 10  =  ABAB  =  4.131 cos θ  =  BC/ACcos 24° 24'  =  BC/100.9107 x 10  =  BCBC  =  9.107

=  (1/2) ⋅ 9.107 ⋅ 4.131

=  9.107 (2.0655)

=  18.81 cm2

Question 2 :

Find the angle made by a ladder of length 5 m with the ground, if one of its end is 4 m away from the wall and the other end is on the wall.

Solution : cos θ  =  Adjacent side / Hypotenuse side

cos θ  =  BC / AC

cos θ  =  4 / 5

cos θ  =  0.8

θ   =  cos 36° 52'

Question 3 :

In the given figure, HT shows the height of a tree standing vertically. From a point P, the angle of elevation of the top of the tree (that is ∠P ) measures 42° and the distance to the tree is 60 metres. Find the height of the tree. Solution :

By finding the length of opposite side, we may find the height of tree.

tan θ  = Opposite / Adjacent

tan θ  = HT/TP

tan 42  = HT/60

HT  =  0.9004 (60)

HT  =  54.02 m

Hence the height of the tree is 54.02 m. After having gone through the stuff given above, we hope that the students would have understood how to find area of triangle with trigonometry word problems.

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