**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.

**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

BC = Adjacent side

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

= (1/2) ⋅ BC ⋅ AB

sin θ = AB/AC sin 24° 24' = AB/10 0.4131 x 10 = AB AB = 4.131 |
cos θ = BC/AC cos 24° 24' = BC/10 0.9107 x 10 = BC BC = 9.107 |

= (1/2) ⋅ 9.107 ⋅ 4.131

= 9.107 (2.0655)

= 18.81 cm^{2}

**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.

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