Download Lecture Notes for Section 6.2

Math Analysis Notes
Section 6.2
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Section 6.2: Trigonometry of Right Triangles
Big Idea: The six trigonometric functions we have studied can be applied to the ratios of sides in any right
triangle to find unknown quantities of those right triangles.
Big Skill: You should be able to identify known and unknown measurements on a right triangle and relate
those quantities using an appropriate trigonometric function.
SOH CAH TOA:
opp
hyp
opp
tan  
adj
1
hyp
sec  

cos 
adj
sin  
adj
hyp
1
adj
cot  

tan  opp
1
hyp
csc 

sin  opp
a2  b2  c2
cos 
To solve a right triangle:
1. Make a sketch of the triangle, label sides and angles consistently (a, b, and c for the legs and
hypotenuse; A and B for the complementary angles), and label the given information.
2. Find a way to relate the unknown parts to the given information using a trig function (sine, cosine, or
tangent) or the Pythagorean Theorem (a2 + b2 = c2). Try to use original given information to minimize
rounding errors.
3. Check your work:
a. Make sure the sides obey the Pythagorean Theorem.
b. Make sure the angles add up to 180.
c. Make sure unused trig functions give the right answers.
d. Make sure that the longest side is opposite the largest angle, and the shortest side is opposite the
smallest angle.
Math Analysis Notes
Section 6.2
Practice:
1. Solve a right triangle given two legs:
2. Solve a right triangle given a leg and a hypotenuse:
3. Solve a right triangle given an angle and an adjacent side:
4. Solve a right triangle given an angle and an opposite side:
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Math Analysis Notes
Section 6.2
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5. Solve a right triangle given an angle and the hypotenuse:
Practice:
6. A road with a 7% grade is 1.2 miles long. How high does the road rise over this length?
7. What is the angle of elevation above the floor of a “body diagonal” across a room that is 15’ by 22’ by
8’?
Math Analysis Notes
Section 6.2
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8. Suppose you measure the angle of elevation to the top of a building to be 46.7, then you step back 115’,
and measure the new angle of elevation to be 38.2. If your measuring instrument is 6’ above the
ground, what is the height of the building?
9. The drawing below shows how to use a pin to check the angle of a dovetail cut. Find dimension x.