Quiz 3.5: Trigonometry

Given the figure on the right, which refers to the angle of elevation? (1 pt)

• $\angle UVS$

• $\angle VST$

• Both $\angle UVS$ and $\angle VST$

• None of the above

Determine the correct formula for the tan ratio of ∠B. (1 pt)

•  $\tan B=\frac{length\ of\ side\ adjacent\ to\ \angle B}{length\ of\ hypotenuse}$  

•  $\tan B=\frac{length\ of\ hypotenuse}{length\ of\ side\ opposite\ to\ \angle B}$  

•  $\tan B=\frac{length\ of\ side\ opposite\ to\ \angle B}{length\ of\ side\ adjacent\ to\ \angle B}$  

•  $\tan B=\frac{length\ of\ side\ opposite\ to\ \angle B}{length\ of\ hypotenuse}$  

Which statement is incorrect? (1 pt)

• The hypotenuse is the longest side in a right triangle.

• The hypotenuse is always the opposite side of the $90\degree$ in a right triangle.

• The Pythagorean theorem applies to all right triangles.

• You can solve for the unknown side in any triangle, if you know the lengths ofthe other two sides, by using the Pythagorean theorem.

In ∆ ABC, AB = 9 cm and BC = 11 cm. Determine the tangent ratio of ∠A to nearest hundredths. (2 pts)

• 0.64

• 0.73

• 1.36

• 1.22

In the figure at the right, ABCD is a rectangle whose perimeter is 30. The length of BE is 12. Determine the measure of ∠E to the nearest degree. (2 pts)

•  $24\degree$  

•  $25\degree$  

•  $26\degree$  

•  $27\degree$  

Use the figure given to find the value of x. (2 pts)

• 10

• 14.1

• 17.3

• 21.5

Use the figure given to find the value of y. (2 pts)

• 10

• 11.5

• 15.2

• 17.3

From a point in the ground 7.62 m from the foot of the tree, the angle of elevation from the top of the tree is  $32\degree$ . Determine the height of the tree to the nearest hundredths. (3 pts)

• 3.81 m

• 6. 46 m

• 4.76 m

• 12.19 m

A 10-foot ladder is placed so as to form an angle of 25° with the wall of a building. How far is the ladder from the base of the building? (3 pts)

• 4.1 ft

• 4.2 ft

• 4.4 ft

• 4.5 ft

The tailgate of a moving van is 3.5 ft above the ground. A loading ramp is attached to the rear of the van at an incline of $10\degree$ . Find the length of the ramp to the nearest tenth foot. (3 pts)