Question

One acute angle of a right angle triangle is double the other if the length of its hypotenuse is 10 cm and its area is

Answer 1

Answer:

21.650 cm^2

Step-by-step explanation:

Let C be the right angle .

sinC = 1 ( sin90°)

Now , Given acute angle is double the other acute angles.

Let the acute angle be x then the other acute angle = x/2 .

Now applying the angle sum property.

x + x/2 + 90 = 180

x+x/2 = 90

3x = 180

x = 60

We get the angles as 60 , 30 , 90 .

Applying the sine rule.

a/sin60 = c/sin90

Given hypotenuse c = 10 .

a/√3/2 = 10/1

2a/√3= 10

a = 5√3

Apply the sine rule again.

b/sin30 = c/sin90

b/1/2 = 10/1

2b = 10

b = 5 .

We now have three sides, hypotenuse = 10 CM and other two sides as 5 , 5√3

Area of triangle = 1/2absinc

= 1/2 ( 5√3) * (5) * 1

= 25√3/2

= 21.650 cm²