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:
5 and 0 between 250 and 300
Answer:
k=4
Step-by-step explanation:
First, we can subtract 3k on both sides. It is ultimately easier to start by subtracting the term with a variable. This would result in 45=5k+25. Then, we can subtract 25 on both sides to get closer to isolating k. This becomes 20=5k. We can then divide by 5 on both sides. This means that k=4.
Answer:
Quantity of heat needed (Q) = 722.753 × 10³
Step-by-step explanation:
According to question,
Mass of water (m) = 40 kg
Change in temperature ( ΔT) = 18°c
specific heat capacity of water = 4200 j kg^-1 k^-1
The specific heat capacity is the amount of heat required to change the temperature of 1 kg of substance to 1 degree celcius or 1 kelvin .
So, Heat (Q) = m×s×ΔT
Or, Q = 40 kg × 4200 × 18
or, Q = 3024 × 10³ joule
Hence, Quantity of heat needed (Q) = 3024 × 10³ joule
In calories 4.184 joule = 1 calorie
So, 3024 × 10³ joule = 722.753 × 10³
