Math Problem Statement

Express cos R as a fraction in simplest terms.

Express cos R as a fraction in simplest terms.

Solution

To find cosR\cos R in the given right triangle PQRPQR, we use the basic definition of cosine in a right triangle:

cosR=adjacent sidehypotenuse\cos R = \frac{\text{adjacent side}}{\text{hypotenuse}}

In the triangle:

  • The angle RR is located at vertex RR.
  • The side adjacent to RR is PQ=60PQ = \sqrt{60}.
  • The hypotenuse is PR=16PR = 16.

Thus, we can express cosR\cos R as:

cosR=PQPR=6016\cos R = \frac{PQ}{PR} = \frac{\sqrt{60}}{16}

Now, simplifying the fraction:

6016=4×1516=21516=158\frac{\sqrt{60}}{16} = \frac{\sqrt{4 \times 15}}{16} = \frac{2\sqrt{15}}{16} = \frac{\sqrt{15}}{8}

So, cosR=158\cos R = \frac{\sqrt{15}}{8} in its simplest form.

Would you like further details or any clarifications?

Here are 5 related questions:

  1. How do you calculate sinR\sin R in this triangle?
  2. What is the value of tanR\tan R for this triangle?
  3. How is the Pythagorean theorem applied in a triangle like this one?
  4. What does the value of sinR\sin R tell you about the angle RR?
  5. How can you express the angle QQ in terms of trigonometric functions?

Tip: Always simplify square roots in expressions for easier calculations!

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Cosine
Right Triangle

Formulas

cosine = adjacent/hypotenuse

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 9-11