Work out:6(10 - 23) + 20
1 answer:
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Answer:
- a ≈ 27.65; B = 28°; c ≈ 19.17
- a ≈ 163.30; B = 120°; c ≈ 59.77
- A = 13°; b ≈ 0.3874; c ≈ 1.3737
Step-by-step explanation:
As long as you're seeking outside help, the use of a suitable tool is appropriate. Many graphing calculators, apps, and web sites are available for solving triangles.
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Here, you're given two angles and a side. The third angle is the difference from 180° of the sum of the other two. For example, in the first problem, ...
B = 180° -A -C = 28°
The missing sides are found using the law of sines. Since you are given a side, use that as the reference, and its opposite angle as the reference angle. Then you have ...
side = sin(opposite angle)×<em>((reference side)/sin(reference angle))</em>
Note that the factor in italics remains the same for both remaining sides.
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In the first problem, this becomes ...
a = sin(112°)·14/sin(28°) ≈ 27.65
c = sin(40°)·14/sin(28°) ≈ 19.17
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The remaining problems are worked in similar fashion.
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<em>Comment on triangle solutions</em>
These are straightforward because you're given two angles. If you're given two sides and an angle, the solution method varies depending on which angle you're given (opposite the long side, the short side, or the unknown side). In the last case, the law of cosines is involved. In the second case, there are likely two solutions. Once you have two angles, you can proceed as above.
Answer:
Tan(b°) = 3/4 = three fourths (C)
Step-by-step explanation:
Triangle JKL is a right angled triangle in which angle K is a right angle and angle L= b°
We would apply SOHCAHTOA from trigonometry to determine the value for each sides.
For ∆JKL
Sin(b°) = opposite/hypotenuse
Sin(b°) = 3/5
Cos(b°) = adjacent/hypotenuse
Cos(b°) = 4/5
Tan(b°) = 3/4
From the above we know the value of each sides of ∆JKL
Find attached the diagram of the above triangle (1)
∆JKL is dilated by a scale factor = 2
Meaning we would multiply each sides of ∆JKL by 2. The values of the new triangle become:
Opposite = 2(3) = 6
Adjacent = 2(4) = 8
Hypotenuse = 2(5) = 10
To find tan(b°) of the new triangle, we would apply tangent ratio
Tan(b°) = opposite/adjacent
Tan(b°) = 6/8
Tan(b°) = 3/4
Find attached the diagram for the new triangle (2)
Diagram 3 shows the drawing of both triangles together.
From the above, we can see the angle doesn't change when a shape is dilated by a scale factor.
Therefore, tan(b°) = three fourths (C)
