section 5-4 applying trig functions objective: students will be able to use trigonometry to find the...
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Example 2: RECREATION A child holding on to the string of a kite gets tired and decides to put the string on the ground and secure it with a brick. The length of the string from the brick to the kite is 240 feet. A) If the angle formed by the string and the ground is °, how high is the kite? We know the angle and the hypotenuse. We want to find the height of the kite (h). h = The height of the kite is about feet.TRANSCRIPT
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Section 5-4
Applying Trig Functions
Objective: Students will be able to use trigonometry to find the measures of the sides of right triangles.
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Example 1:
If B = 42° and a = 12, find c, b, and A.
You know the measure of the side adjacent the angle.
The cosine function relates the side adjacent to the angle and the hypotenuse.
cos𝜃=𝑠𝑖𝑑𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
cos 42 °=12𝑐𝑐 cos 42°=12𝑐=
12cos 42 °
C = 16.1476
C
tan𝜃=𝑠𝑖𝑑𝑒𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑠𝑖𝑑𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
tan 42 °= 𝑏12
12 tan 42°=𝑏10.8048=𝑏𝑏≈10.8
A + B + C = 180
A + 42 + 90 = 180
A = 48
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Example 2:RECREATION A child holding on to the string of a kite gets tired and decides to put the
string on the ground and secure it with a brick. The length of the string from the brick to the kite is 240 feet.
A) If the angle formed by the string and the ground is 50.275°, how high is
the kite?
We know the angle and the hypotenuse. We want to findthe height of the kite (h).
sin 𝜃=𝑠𝑖𝑑𝑒𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
sin 50.275= h240
240sin 50.275=h
h = 184.589The height of the kite is about 184.6 feet.
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B) What is the horizontal distance between the kite and the brick?
Her we want to know the side adjacent the angle. So we will use the cosine function.
cos𝜃=𝑠𝑖𝑑𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
cos 50.275= 𝑑240
240 cos 50.275 = d
D = 153.3848
The horizontal distance between the brick and the kite is about 153.4 feet.