Trigonometric Ratios
What does SOH stand for in SOHCAHTOA?
Sine = opposite ÷ hypotenuse
What is the longest side of a right triangle called?
Hypotenuse
What do we call the angle formed when looking upward from a horizontal line?
Angle of elevation
From which direction are three-figure bearings measured clockwise?
North
What is the formula for the semiperimeter of a triangle?
s = (a + b + c) ÷ 2
Which tool is commonly used to measure angles of elevation in fieldwork?
Clinometer
Which trigonometric ratio compares the adjacent side to the hypotenuse?
Cosine
Which law is commonly used to find the third side of an oblique triangle when two sides and their included angle are known?
Law of Cosines
What angle is formed when a person on a rooftop looks downward at a car?
Angle of depression
What is the three-figure bearing for due south?
180°
Which formula finds the area of a triangle using two sides and their included angle?
Area = ½ab sin C
Which law is useful when two angles and one side of an oblique triangle are known?
Law of Sines
A right triangle has an opposite side of 9 cm and a hypotenuse of 15 cm. What is sin θ?
0.6
A right triangle has legs of 5 cm and 12 cm. Find its hypotenuse.
13 cm
A student stands 12 m from a wall and sees its top at 45°. Assuming eye level is at ground level, how tall is the wall?
12 m
A ship travels due west. What is its bearing?
270°
A triangle has side lengths 6 cm, 8 cm, and 10 cm. What is its semiperimeter?
12 cm
A 10 m ladder leans against a wall at 30° to the ground. How high does it reach?
5 m
A ramp rises 4 m over a horizontal distance of 10 m. Which trigonometric ratio would you use to find its angle?
Tangent
A triangle has side lengths 4 cm, 6 cm, and 11 cm. Can it form a triangle?
No
A kite is 20 m horizontally from an observer and 20 m above the observer's eye level. What is the angle of elevation?
45°
A boat travels on a bearing of 045°. Which general direction is it heading?
Northeast
Find the area of a triangle with sides 6 cm and 10 cm and an included angle of 30°.
15 cm²
Two triangles have the same side lengths of 10 cm and 12 cm, but their included angles are 30° and 90°. Which triangle has the larger area?
The triangle with the 90° included angle.
A student says cos θ = opposite ÷ hypotenuse. Is the student correct?
No. Cosine = adjacent ÷ hypotenuse.
A triangle has angles of 45°, 65°, and 70°. Is it a right or oblique triangle?
Oblique triangle
A surveyor calculates the top of a pole is 10 m above the instrument. The instrument is 1.4 m above ground. What is the pole's total height?
11.4 m
A ship travels on a bearing of 120°. What is its reverse bearing?
300°
Using Heron's formula, find the area of a triangle with sides 5 cm, 5 cm, and 6 cm.
12 cm²
You want to measure the height of a building using trigonometry. What three measurements or pieces of information should you collect?
Horizontal distance, angle of elevation, and observer/instrument height.