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7.5 Apply the Tangent Ratio. Hubarth Geometry. Sine, cosine and tangent are the three trigonometric functions we use in Geometry. SOH CAH TOA is a phrase that we use to help us remember the ratios of these functions. SOH - Sin = CAH - Cos = TOA - Tan =. Tangent Ratio - PowerPoint PPT Presentation
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7.5 Apply the Tangent Ratio
HubarthGeometry
Sine, cosine and tangent are the three trigonometric functions we use in Geometry. SOH CAH TOA is a phrase that we use to help us remember the ratios of these functions.
SOH - Sin =
CAH - Cos =
TOA - Tan =
Tangent Ratio
Let be a right triangle with acute angle A.The tangent of angle A (written as tan A) isdefined as follows:
tan A = =
tan A =
B
C A
legopposite A
hypotenuse
leg adjacent to A
Find tan S and tan R. Write each answer as a fraction and as a decimal rounded to four places.
Ex 1 Find Tangent Ratios
tan S = = =
tan𝑅=𝑜𝑝𝑝𝑎𝑑𝑗
=𝑆𝑇𝑅𝑇
=1880
=.2250
Find the value of x.
Ex 2 Find a Leg Length
tan 32 =
opp
adj
tan ¿oppadj
𝑥 ∙ tan 32=11𝑥∙𝑥
𝑥 ∙ tan 32=11
𝑥 ∙𝑡𝑎𝑛32𝑡𝑎𝑛32
=11
𝑡𝑎𝑛32
x = 17.6
Ex 3 Estimate height Using Tangent
Find the height h of the lamppost to the nearest inch.
tan 70=h40
40 ∙ tan 70=h40∙ 40
40 tan 70 = h
h= 109.9 in
Find tan J and tan K. Round to four decimal places.
tan J = 0.75tan K = 1.33
tan J = 0.53tan K = 1.88
Practice
Find the value of x. Round to the nearest tenth.
x = 12.2 x = 19.3