CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 4. Basic Triangle Trigonometry

tanα= 507 h+x

tanβ=hx

Both of these equations can be solved forhand then set equal to each other to findx.

h=tanα( 507 +x) =xtanβ

507 tanα+xtanα=xtanβ

507 tanα=xtanβ−xtanα

507 tanα=x(tanβ−tanα)

x=tan507 tanβ−tanαα= 507 tan 21.^567

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tan 25. 683 ◦−tan 21. 567 ◦≈^228.^7 meters

Since the problem asked for the height, you need to substitutexback and solve forh.
h=xtanβ= 228 .7 tan 25. 683 ◦≈ 109. 99 meters
Example C
Given a triangle with SSS or SAS you know to use the Law of Cosines. In triangles where there are corresponding
angles and sides like AAS or SSA it makes sense to use the Law of Sines. What about ASA?
Given∆ABCwithA=π 4 radians,C=π 6 radiansandb= 10 inwhat isa?
Solution:First, draw a picture.

The sum of the angles in a triangle is 180◦. Since this problem is in radians you either need to convert this rule to
radians, or convert the picture to degrees.

A=π 4 ·^180

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π =^45

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C=π 6 ·^180

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π =^30

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The missing angle must be^6 B= 105 ◦. Now you can use the Law of Sines to solve fora.

sin 105◦

10 =

sin 45◦

a

a=10 sin 45

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sin 105◦ ≈^7.^32 in