Indirect Measurement with Trig

Right Triangle Trigonometry

Finding missing sides when you have an angle to work with

Fill in the Blank

Warmup: The leg of a right triangle is 24, and the hypotenuse is 25. What is the length of the other leg?

Multiple Choice

Warmup: A triangle has sides 6, 10, and 12.

• Acute

• Obtuse

• Right

• Not even a triangle

SohCahToa

• All three trig functions are give fraction answers.

• Sine = opposite/hypotenuse

• Cosine = adjacent/hypotenuse

• Tangent = opposite/adjacent

SohCahToa Example

• Sine = OPP/HYP

• Sin(A) = 21/35

• Tangent = OPP/ADJ

• Tan(C) = 28/21

• You don't ever do a trig function from the right angle

Multiple Choice

SohCahToa. What is Sin(A)?

• 30/16

• 16/34

• 30/34

• 16/30

Multiple Choice

SohCahToa. What is Cos(A)?

• 16/30

• 16/34

• 30/16

• 30/34

Multiple Choice

SohCahToa. What is Tan(A)?

• 27/36

• 36/45

• 27/45

• 36/27

What we really want to do

• We want to calculate a side when we have a reference angle to work with.

• You need a right triangle

• And one side and one angle

SohCahToa

• To find the height of the building, we use tangent

• We want to know the height (opposite) and we already know the ground distance (adjacent)

• O & A are tangent's letters

Toa

• ​Call the opposite side, the height of the building, x

• ​Tangent is opposite over adjacent -- what we want, and what we know -- so pick tangent

• tan(55) = x/57

• 1.428 = x/57 [calculator tan(57)]

• 81.396 = x [mult. both sides by 57]

• The height of the building is 81.396​

Multiple Choice

SohCahToa. Find x.

• 5.3

• 4.9

• 3.8

• 7

Multiple Choice

SohCahToa. Find x.

• 18.0

• 21.8

• 17.1

• 25

Multiple Choice

SohCahToa. Find x.

• 35.5

• 37.2

• 41.1

• 50.7