Multiple Choice
Without using a calculator, determine all values of P in the interval with the following trigonometric function value.
2. Trigonometric Functions on Right Triangles
Special Right Triangles
Struggling with Trigonometry?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Given the triangle below, determine the missing side(s) without using the Pythagorean theorem (make sure your answer is fully simplified).
A
B
C
D
Verified step by step guidance1
Identify the type of triangle: The given triangle is a right triangle with one angle measuring 45 degrees. This indicates that it is a 45-45-90 triangle, which is an isosceles right triangle.
Recall the properties of a 45-45-90 triangle: In a 45-45-90 triangle, the legs are congruent, and the hypotenuse is \( \sqrt{2} \) times the length of each leg.
Given that both legs of the triangle are 9 units, use the property of 45-45-90 triangles to find the hypotenuse. The formula for the hypotenuse \( x \) is \( x = 9 \times \sqrt{2} \).
Simplify the expression for the hypotenuse: \( x = 9 \sqrt{2} \). This is the length of the hypotenuse in its simplest form.
Verify the solution: Check that the calculated hypotenuse \( x = 9 \sqrt{2} \) is consistent with the properties of a 45-45-90 triangle, ensuring that the solution is correct.
Related Videos
Related Practice
Special Right Triangles practice set
Problem sets built by lead tutorsExpert video explanations