Answer:
388.5yd²
Step-by-step explanation:
We have Triangle TUV
In the question, we are given already
Angle U = 32°
Angle T = 38°
Angle V = ???
Side t = 31yd
Side u = ?
Side v = ?
Area of the triangle= ?
Step 1
We find the third angle = Angle V
Sum of angles in a triangle = 180°
Third angle = Angle V = 180° - (32 + 38)°
= 180° - 70°
Angle V = 110°
Step 2
Find the sides u and v
We find these sides using the sine rule
Sine rule or Rule of Sines =
a/ sin A = b/ Sin B
Hence for triangle TUV
t/ sin T = u/ sin U = v/ sin V
We have the following values
Angle T = 38°
Angle U = 32°
Angle V = 110°
We are given side t = 31y
Finding side u
u/ sin U= t/ sin T
u/sin 32 = 31/sin 38
Cross Multiply
sin 32 × 31 = u × sin 38
u = sin 32 × 31/sin 38
u = 26.68268yd
u = 26.68yd
Finding side x
v / sin V= t/ sin T
v/ sin 110 = 31/sin 38
Cross Multiply
sin 110 × 31 = v × sin 38
v = sin 110 × 31/sin 38
v = 47.31573yd
v = 47.32yd
To find the area of triangle TUV
We use heron formula
= √s(s - t) (s - u) (s - v)
Where S = t + u + v/ 2
s = (31 + 26.68 + 47.32)/2
s = 52.5
Area of the triangle = √52.5× (52.5 - 31) × (52.5 - 26.68 ) × (52.5 - 47.32)
Area of the triangle = √150967.6032
Area of the triangle = 388.5454973359yd²
Approximately to the nearest tenth =388.5yd²
Answer:
x > - 1
Step-by-step explanation:
Given
- 3x - 5 < - 2 ( add 5 to both sides )
- 3x < 3
Divide both sides by - 3, reversing the symbol as a result of dividing by a negative quantity
x > - 1
Answer:30
Step-by-step explanation:
3/10x=90
Use reciprocal to multiple both sides
x=answer
Answer:4
Step-by-step explanation:
Answer:
7.2 km
Step-by-step explanation:
Distance between Brookfield to Seaside = 20.4 km
Distance between Yardley and Seaside = 13.2 km
Let distance between Brookfield to Yardley be x.
Thus:
x + 13.2 km = 20.4 km
Subtract 13.2 from each side
x = 20.4 - 13.2
x = 7.2
Distance from Brookfield to Yardley is 7.2 km
