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