Question

I'm confused on how to solve the triangle. can someone help me please?

Answer 1

Hello from MrBillDoesMath!

Answer:

The length of the remaining side is sqrt (105.79). (Approximately 10.29 )

Discussion:

This is a right triangle (meaning it has a 90 degree angle) so the Pythagorean theorem applies. This states that

a^2 + b^2 = c^2

where "a" and "b" are the sides of the triangle and "c" is the hypotenuse (longest side). Suppose we call the side in the diagram without a length "a". Then by Pythagoras

a^2 + (3.9)^2 = 11^ 2 =>

a^2 + 15.21 = 121 => subtract 15.21 from both sides

a^2 = 121 - 15.21 = 105.79 => take the square root of both sides

a = sqrt (105.79) which is approximately 10.29

Thank you,

MrB

Answer 2

b = 10.28542658

Explanation:

This is a right triangle, so we can use the Pythagorean theorem

a^2 +b^2 =c^2

The legs are a and b and the hypotenuse is c

We know one of the legs and the hypotenuse

3.9^2 + b^2 = 11^2

15.21 + b^2 = 121

Subtract 15.21 from each side

15.21-15.21 + b^2 = 121-15.21

b^2 = 105.79

Take the square root of each side

sqrt(b^2) = sqrt(105.79)

b = 10.28542658