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# Right Triangle Formula

Right triangle is a triangle whose one of the angle is right angle. Also the sum of other two angles is equal to 90 degrees. Right Triangle Formula is used to calculate the area, perimeter, unknown sides and unknown angles of the right triangle. Right Triangle Formula is given below as, The unknown sides in a right triangle can be calculated using the Pythagoras formula. The unknown angles in a right triangle can be calculated using the sine, cosine and tangent formulas. Related Calculators Area of a Right Triangle Calculator

## Right Triangle Problems

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Some solved problems on right triangle are given below:

### Solved Examples

Question 1: Find the length of the hypotenuse of the right triangle if the length of the other two sides are 5 cm and 7 cm. Also calculate the area and perimeter of the triangle ?
Solution:

Given,
a = 5 cm
b = 7 cm

using the Pythagoras formula,
c2 = a2 + b2
c2 = (5 cm)2 + (7 cm)2
c2 = 25 cm2 + 49 cm2
c2 = 74 cm2
c = 8.602 cm

Area of the right triangle
= $\frac{1}{2}$ab
= $\frac{1}{2}$ $\times 5 cm \times 7 cm$
= 17.5 cm2

Perimeter of the right triangle
= a + b + c
= 5 cm + 7 cm + 8.602 cm
= 20.602 cm

Question 2: Find the angles of the right triangle ABC if ∠B is 90o and the length of the sides of the triangle are AB = 12 cm, BC = 9 cm and CA = 15 cm ?
Solution:

Given,
∠B = 90o
AB = b = 12 cm
BC = a = 9 cm
CA  = c = 15 cm

∠A = sin-1 $\big(\frac{a}{c}\big)$
∠A = sin-1 $\big(\frac{9}{15}\big)$
∠A = 36.87o

∠C = sin-1 $\big(\frac{b}{c}\big)$
∠C = sin-1 $\big(\frac{12}{15}\big)$
∠C = 53.13o

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