Question

Solve for the variable when the hypotinuse is 10 and you know one angle, 42

Answer 1

Answer: The other sides are 6.7 units and 7.4 units

Step-by-step explanation: Every right angled triangle can be solved by use of the trigonometric ratios. We can use the sine, cosine or tangent depending on which sides are given. If one angle has been given as 42 degrees, then the side opposite that angle can be calculated as,

Sin 42 = opposite/hypotenuse

Sin 42 = a/10

We cross multiply and we now have

Sin42 x 10 = a

0.6691 x 10 = a

a = 6.69 (which is approximately 6.7)

If one of the other two angles was given as 42, then the third angle would be calculated as 180 - (90 + 42) {sum of angles in a triangle equals 180} and that equals 48.

To calculate the third side,

Sin48 = opposite/hypotenuse

Sin48 = y/10

We cross multiply and we have

Sin48 x 10 = y

0.7431 x 10 = y

y = 7.43 (which is approximately 7.4)

Therefore the two other sides are 6.7 and 7.4