Problem 1 Writing Trigonometric Ratios

What are the sine, cosine, and tangent ratios for ∠ T ? angle t question mark

sin   T = opposite hypotenuse = 8 17 cos   T = adjacent hypotenuse = 15 17 tan   T = opposite adjacent = 8 15 table with 3 rows and 2 columns , row1 column 1 , sine t , column 2 equals . fraction opposite , over hypotenuse end fraction . equals , 8 seventeenths , row2 column 1 , cosine t , column 2 equals . fraction adjacent , over hypotenuse end fraction . equals , 15 over 17 , row3 column 1 , tangent t , column 2 equals . fraction opposite , over adjacent end fraction . equals , 8 fifteenths , end table

✓ Got It?

1. Use the triangle in Problem 1. What are the sine, cosine, and tangent ratios for ∠ G ? angle g question mark

Problem 2 Using a Trigonometric Ratio to Find Distance

Landmarks In 1990, the Leaning Tower of Pisa was closed to the public due to safety concerns. The tower reopened in 2001 after a 10-year project to reduce its tilt from vertical. Engineers' efforts were successful and resulted in a tilt of 5 ° , 5 degrees comma reduced from 5 . 5 ° . 5 . 5 degrees . Suppose someone drops an object from the tower at a height of 150 ft. How far from the base of the tower will the object land? Round to the nearest foot.

The given side is adjacent to the given angle. The side you want to find is opposite the given angle.

tan   5 ° = x 150 Use the tangent ratio . x = 150 ( tan 5 ° ) Multiply each side by  150. 150 tan 5 enter Use a calculator . x ≈ 13.12329953   table with 4 rows and 3 columns , row1 column 1 , tangent 5 degrees , column 2 equals , x over 150 , column 3 cap usethetangentratio . . , row2 column 1 , x , column 2 equals 150 . open , tangent 5 degrees , close , column 3 cap multiplyeachsideby . 150. , row3 column 1 , 150 , begin box , tangent , end box , column 2 5 , begin box , enter , end box , column 3 cap useacalculator . . , row4 column 1 , x , column 2 almost equal to . 13.12329953 , column 3 , end table

The object will land about 13 ft from the base of the tower.