‘According to this diagram, what is tan 62°? A 17/15 B 8/17 C 15/17 D 8/15 E 17/8 F 15/8 cording to this diagram, what is tan 62″ 62 17 28′ 90 15 A 17 0 15’
The Correct Answer and Explanation is:
To determine tan 62° from the given right triangle, we must recall the trigonometric definition of tangent:tan(θ)=oppositeadjacent\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}tan(θ)=adjacentopposite
For θ = 62°, based on the triangle in the diagram:
- The opposite side to the 62° angle is labeled 8 (the vertical side).
- The adjacent side to the 62° angle is labeled 15 (the horizontal side).
Now apply the formula:tan(62°)=815\tan(62°) = \frac{8}{15}tan(62°)=158
So the correct answer is:
D. 815\frac{8}{15}158
Explanation
Understanding trigonometric ratios in right triangles is essential in geometry and trigonometry. In a right triangle, the tangent function relates an acute angle to the ratio of the lengths of two specific sides: the side opposite the angle and the side adjacent to it. Specifically, for any angle θ in a right triangle:tan(θ)=length of the side opposite θlength of the side adjacent to θ\tan(\theta) = \frac{\text{length of the side opposite θ}}{\text{length of the side adjacent to θ}}tan(θ)=length of the side adjacent to θlength of the side opposite θ
In this triangle, three angles are given: 28°, 62°, and 90°. The angle 90° tells us that it is a right triangle. The angle in question is 62°. We are asked to calculate the tangent of 62°, which means we are interested in the ratio of the side opposite the 62° angle to the side adjacent to it.
By looking at the triangle, we can identify the side opposite to the 62° angle as the vertical side marked with length 8. The side adjacent to the 62° angle is the horizontal side with length 15. The hypotenuse, labeled 17, is not used for tangent but would be used for sine or cosine.
By substituting the known values into the tangent formula:tan(62°)=815\tan(62°) = \frac{8}{15}tan(62°)=158
This ratio is exact as per the triangle’s given dimensions, and it matches option D. Other choices like 17/15 or 15/8 would be incorrect because they either use the hypotenuse or reverse the ratio. Therefore, the correct answer is clearly 8 divided by 15, which matches option D.
