A right triangle has one angle that measures 23 degrees. The adjacent leg measures 27.6 cm and the hypotenuse measures 30cm. What is the approximate area of the triangle?
Mathematics · High School · Thu Feb 04 2021
Answered on
Given:
A right triangle has one angle that measures 23 degrees. The adjacent leg measures 27.6 cm and the hypotenuse measures 30cm.
a = 27.6
b = ?
c = 30 cm
Determine the area of the triangle.
Formula for the area of the right triangle:
A = ab/2
Formula for the Pythagorean theorem.
c^2 = a^2 + b^2
b = (c^2 - a^2)^½
Solution:
Find first b, by substituting the given values of a and c to the equation.
b = (c^2 - a^2)^½
b = (30^2 - 27.6^2)^½
b = (900 - 761.76)^½
b = (138.24)^½
b = 11.75 cm
Equate the values of a and b to the formula for the area of the right triangle.
A = (27.6 cm)(11.75 cm)/2
A =324.3/2
A = 162.15 cm^2
Final answer:
A = 162.15 cm^2