1. 7.5 Apply the Tangent Ratio
Hubarth
Geometry

2. SOH - Sin = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
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 = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
CAH - Cos = 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
TOA - Tan = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
Tangent Ratio
Let ∆𝐴𝐵𝐶 be a right triangle with acute angle A.
The tangent of angle A (written as tan A) is
defined as follows:
tan A = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑒𝑔 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝐴 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑙𝑒𝑔 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝐴 = 𝐵𝐶 𝐴𝐶
tan A = 𝐵𝐶 𝐴𝐶 B
hypotenuse
leg
opposite A C
leg
adjacent to A A

3. Ex 1 Find Tangent Ratios
Find tan S and tan R. Write each answer as a fraction and as a decimal rounded to four places.
tan S = 𝑜𝑝𝑝 𝑎𝑑𝑗 = 𝑅𝑇 𝑆𝑇 = =4.4444
tan 𝑅= 𝑜𝑝𝑝 𝑎𝑑𝑗 = 𝑆𝑇 𝑅𝑇 = =.2250

4. Ex 2 Find a Leg Length
Find the value of x.
opp
adj
tan = opp adj
tan 32 = 11 𝑥
𝑥∙ tan 32= 11 𝑥 ∙𝑥
𝑥∙ tan 32=11
𝑥∙𝑡𝑎𝑛32 𝑡𝑎𝑛32 = 11 𝑡𝑎𝑛32
x = 17.6

5. Ex 3 Estimate height Using Tangent
Find the height h of the lamppost to the nearest inch.
tan 70= ℎ 40
40∙ tan 70= ℎ 40 ∙40
40 tan 70 = h
h= in

6. Practice
Find tan J and tan K. Round to four decimal places.
tan J = 0.53
tan K = 1.88
tan J = 0.75
tan K = 1.33
Find the value of x. Round to the nearest tenth.
x = 12.2
x = 19.3