In a right triangle
c=90 degrees a=52 degrees b = 38 degrees
the base length =11
What is the hypotenuse length?
a-6.8
b-8.7
c-14.0
d-17.9
my answer is 17.9 d
If the leg of length 11 is adjacent to angle a, you are correct.
thank you
To find the hypotenuse length of a right triangle, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we are given the angles of the triangle and the length of one side (the base), so we need to find the length of the other side (the perpendicular or height) in order to calculate the hypotenuse length.
Since the given angles are 52 degrees and 38 degrees, we know that the third angle (opposite the base) must be 90 - (52 + 38) = 90 - 90 = 0 degrees. However, a triangle cannot have an angle of 0 degrees, so there seems to be an error in the given information.
If we assume that the angles given are angles a and b, and angle c is the right angle (90 degrees), then we can use the sine and cosine ratios to find the missing side length.
Given a = 52 degrees, b = 38 degrees, and the base length = 11:
- The side opposite angle a is the perpendicular, which we can denote as side A.
- The side opposite angle b is the base, which we are given as 11.
- The hypotenuse is the side opposite the right angle (c) and we need to find its length.
Using trigonometric ratios, we can find the length of side A:
sin(a) = A / hypotenuse
A = sin(a) * hypotenuse
cos(a) = 11 / hypotenuse
Since sin(a) = sin(52) and cos(a) = cos(52), we can find the values using a scientific calculator or table.
Given that the base length is 11, we can substitute the values in the equations and solve for the hypotenuse:
A = sin(52) * hypotenuse
cos(52) = 11 / hypotenuse
Rearranging the second equation gives us:
hypotenuse = 11 / cos(52)
Using a scientific calculator or approximating cos(52) to a decimal value, we can calculate the value for the hypotenuse.
Based on the available answer choices, the closest value to the calculated hypotenuse should be the correct answer. In this case, the closest value is 17.9 (option d). Therefore, the correct answer is d-17.9.