The tangent of a certain acute angle θis 5 . a. Make a right triangle with an acute angle θthat

step 1 I'm given a trig ratio that is cosine of theta is one fifth. We're asked to first of all draw a

The tangent of a certain acute angle θis 5 . a. Make a right...

The tangent of a certain acute angle $\theta$ is 5 . a. Make a right triangle with an acute angle $\theta$ that has a tangent of 5. Suggestion: Note that $5=\frac{5}{1}$, and choose convenient lengths for the opposite and adjacent sides. b. Find the length of the hypotenuse in the right triangle you made in part a. c. Find $\cos \theta$.

The tangent of a certain acute angle $\theta$ is 5 .
a. Make a right triangle with an acute angle $\theta$ that has a tangent of 5. Suggestion: Note that $5=\frac{5}{1}$, and choose convenient lengths for the opposite and adjacent sides.
b. Find the length of the hypotenuse in the right triangle you made in part a.
c. Find $\cos \theta$.

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Key Concepts

Trigonometric Ratios

Trigonometric ratios define the relationships between the sides of a right triangle relative to one of its acute angles. In this context, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side, while the cosine is defined as the ratio of the adjacent side to the hypotenuse.

Right Triangle Construction

A right triangle is used to visually and numerically represent the relationships described by the trigonometric ratios. By choosing specific values for the sides based on a given ratio (such as setting the opposite side to 5 and the adjacent side to 1 for a tangent of 5), one can easily determine other properties of the triangle.

Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. It states that the sum of the squares of the two legs (the sides forming the right angle) is equal to the square of the hypotenuse. This theorem is essential for calculating the hypotenuse when the lengths of the other two sides are known.

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