If x is a positive acute angle and cos x = 3/5, find the value of sinx.
1 answer:
X is a positive acute angle. That means x is located in the first quadrant and has positive value in sin, cos, tan.
The formula of trigonometry ratio
cos x =
sin x =
From the formula of cosine
cos x =
from the formula above, adjacent side is 3 units, and hypotenuse is 5 units
Draw a right triangle to illustrate the location of the sides. See image attached.
To find the ratio of sine, we need to find the length of opposite side using pythagorean theorem
3² + (opposite)² = 5²
9 + (opposite)² = 25
(opposite)² = 25 - 9
(opposite)² = 16
opposite = 4
The length of opposite side is 4 units
Find sin x
sin x =
sin x =
The formula of trigonometry ratio
cos x =
sin x =
From the formula of cosine
cos x =
from the formula above, adjacent side is 3 units, and hypotenuse is 5 units
Draw a right triangle to illustrate the location of the sides. See image attached.
To find the ratio of sine, we need to find the length of opposite side using pythagorean theorem
3² + (opposite)² = 5²
9 + (opposite)² = 25
(opposite)² = 25 - 9
(opposite)² = 16
opposite = 4
The length of opposite side is 4 units
Find sin x
sin x =
sin x =
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A fisherman can row upstream at 4 mph and downstream at 6 mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. The distance of how far the fisherman row if the entire trip took 2 hours is 9.6 miles
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The speed of an object refers to the change of the object's distance within a specified time.
Mathematically, we can have;
Distance = speed × time
From the information given;
- The fisherman row upstream for 4 miles/ hour.
- The distance covered by the fisherman = 4 × t₁ ----- (1)
- The fisherman row downstream at 6 miles/ hour
- The distance covered by the fisherman = 6 × t₂ ------ (2)
- SInce it took the entire trip 2 hours, we can infer that:
- t₁ + t₂ = 2
- t₂ = 2 - t₁
From equation (2), replace the above value of t₂ into equation (2)
- d = 6 t₂
- d = 6(2 - t₁)
- d = 12 - 6t₁
From equation (1)
- d = 4 t₁
Equation both distance together, we have:
- 12 - 6t₁ = 4t₁
- 12 = 4t₁ + 6t₁
- 12 = 10t₁
- t₁ = 12/10
- t₁ = 1.2 hours
From t₂ = 2 - t₁
- t₂ = 2 - 1.2
- t₂ = 0.8 hours
From d = 4t₁
Replace t₁ with 1.2 hours
- d = 4(1.2 hours)
- d = 4.8 miles
Also, from d = 6t₂
- d = 6(0.8)
- d = 4.8 miles
Therefore, we can conclude that the distance of how far the fisherman row if the entire trip took 2 hours is (4.8+4.8) miles = 9.6 miles
Learn more about distance here:
Answer:
Total paper required = 165 cm²
Step-by-step explanation:
Paper required to cover the entire block = (Surface area of the prism at the base - area of the top of the prism) + Lateral surface area of the pyramid
Surface area of the rectangular prism = 2(lb + bh + hl)
(here l, b, h are the length, width and height respectively)
= 2(5×5 + 5×4 + 4×5)
= 2(25 + 20 + 20)
= 2×65
= 130 cm²
Area of the top of the prism = (side)²
= 5²
= 25 cm²
Lateral area of the square pyramid = 4 × Area of one lateral side
= 4 ×
= 4 ×
= 60 cm²
Total paper required = (130 - 25) + 60
= 105 + 60
= 165 cm²