Title (primary CCSS Math with Title)
CCSS.MATH.CONTENT.HSG-SRT.C.8.
- Similarity, Right Triangles, & Trigonometry
Alignment to Content Standards
Define trigonometric ratios and solve problems involving right triangles
Use trigonometric ratios and Pythagorean Theorem to solve right triangles in applied problems.
Task
Word Problem:
Isabel just planted a new tree and attaches a guy wire to help support the tree while its roots take hold. A 6-foot wire is attached to the tree and to a pole in the ground. From the pole in the ground the angle of elevation of the connection with the tree is 52º. Find to the nearest tenth of a foot, the height of the connection point on the tree. Use the diagram below to help model the problem. Label diagram if desired.
Figure 1
Commentary
The purpose of this task is so students can apply their combination of skills of similar triangles, ratios, right triangle trigonometry and their knowledge on the Pythagorean theorem to solve problems in mathematics related to real life scenarios.
Solution
The “angle of elevation” is from the ground up.
It is supposed that the tree is vertical which makes it perpendicular with the ground.
This problem is a sine problem since it involves opposite and hypotenuse.
sin52°=h/6; 6sin52°=h; h≈4.7 feet