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:
2,360
Step-by-step explanation:
18% of 2,000 is 360
(0.18)*(2,000)=360
2,000 + 360 = 2,360
Answer: 1 : 1.48
Step-by-step explanation:
Adam was able to change £400 into 592 francs which means that the British pound is stronger because it was able to buy more Swiss francs.
The exchange rate can be gotten using direct proportion:
400 : 592
1 : x
Cross multiply:
400x = 592
x = 592/400
x = 1.48
Exchange rate is:
= 1 : 1.48
Answer:
<em>Pizza eaten together: 5/6,</em>
<em>Pizza left over: 1/6</em>
Step-by-step explanation:
~ If Ellen ate 2/4th of the pizza and John ate 1/3 of the pizza, provided that the pizza counts as a whole ( 1 )... ~
1. Let us simplify 2/4th to be ⇒ 1/2, through simple algebra
2. To see how much they ate together we would neglect that the pizza counts as a whole but simply add 1/2 by 1/3rd.
3. Through simple algebra: 1/2 + 1/3 = 3/6 + 2/6 = <em>Pizza eaten together: 5/6</em>
4. Now to find out how much pizza was left over, we would need the fact that a pizza ⇒ 1 whole. It would be that 1 - 1/2 - 1/3 ⇒ Pizza left over, through the <em>Partition Postulate. </em>In fact, the pizza left over would simply be 1 whole - the pizza eaten together ( 5/6 ).
5. Through algebra: 1 - 1/2 - 1/3 = 1 - 5/6 = <em>Pizza left over: 1/6</em>
Answer:
c
Step-by-step explanation:
