Construct a right angled triangled whose one side is 7.3cm and sum of other two sides is 13.5
Answers
Answer:
Solve triangle problems using the sine law . A tutorial with problems, detailed solutions and exercises with answers. The ambiguous case of the sine law, where two sides and one angle are given, is also considered (problems 3 and 4).
Problem 1
A triangle ABC has angle A = 106 o, angle B = 31 o and side a = 10 cm. Solve the triangle ABC by finding angle C and sides b and c.(round answers to 1 decimal place).
Solution to Problem 1:
Use the fact that the sum of all three angles of a triangle is equal to 180 o to write an equation in C.
A + B + C = 180 o
Solve for C.
C = 180 o - (A + B) = 43 o
Use sine law to write an equation in b.
a / sin(A) = b / sin(B)
Solve for b.
b = a sin (B) / sin(A) = (approximately) 5.4 cm
Use the sine law to write an equation in c.
a / sin(A) = c / sin(C)
Solve for c.
c = a sin (C) / sin(A) = (approximately) 7.1 cm
Problem 2
The angle of elevation to the top C of a building from two points A and B on level ground are 50 degrees and 60 degrees respectively. The distance between points A and B is 30 meters. Points A, B and C are in the same vertical plane. Find the height h of the building(round your answer to the nearest unit).
diagram problem 2
Solution to Problem 2:
We consider triangle ABC. Angle B internal to triangle ABC is equal to
B = 180 o - 60 o = 120 o
In the same triangle, angle C is given by.
C = 180 o - (50 o + 120 o) = 10 o
Use sine law to find d.
d / sin(50) = 30 / sin(10)
Solve for d.
d = 30 *sin(50) / sin(10)
We now consider the right triangle.
sin (60) = h / d
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Solve for h.
h = d * sin(60)
Substitute d by the expression found above.
h = 30 *sin(50) * sin(60) / sin(10)
Use calculator to approximate h.
h = (approximately) 115 meters.
Problem 3
A triangle ABC has side a = 12 cm, side b = 19 cm and angle A = 80 o (angle A is opposite side a). Find side c and angles B and C if possible.(round answers to 1 decimal place).
Solution to Problem 3:
Use sine law to write an equation in sin(B).
a / sin(A) = b / sin(B)
Solve for sin(B).
sin (B) = (b / a) sin(A) = (19/12) sin(80) = (approximately) 1.6
No real angle B satisfies the equation
sin (B) = 1.6
The given problem has no solution.
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