Download MR12 Lsn 84 - Forest Hills High School

Aim: How do we find the area of
triangle using trigonometry?
Do Now: In the diagram, ∆ABC and h is the
height
1. Find the area of ∆ABC
2. Find sin C
A
b
C
HW: p.563 # 4,6,10,12,19,20
h
a
c
B
Area of triangle
1
K  ab sin C
2
We use K to represent the area of a triangle
so not to confuse A with the angle A.
This formula can be used to find the area of
triangle, if the lengths of two sides and the
included angle are known.
Application:
1. Given the triangle ABC, with AC = 12, BC = 18
and C = 94. Find the area to nearest integer.
108
2. In the diagram, the parallelogram ABCD, find its
exact area.
D
C
10
80 3
A
16
B
A farmer has a triangular field where two sides
measure 450 yards and 320 yards. The angle
between these two sides measures 80. The farmer
wishes to use an insecticide that costs $4.50 per 100
square yards or any part of 100 yards. What will it
cost to use insecticide on this field?
$3195
A triangle has two sides of 30 meters and 26 meters,
and the angle between them is an obtuse angle. If the
area of the triangle is 300 square meters, find the
measure of the obtuse angle to the nearest degree.
130º
Two observers are 600 ft apart on opposite sides of a
flagpole. The angles of elevation from the observers
to the top of the pole are 19º and 21º. Find the height
of the flagpole.