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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The size of angle PRQ is 15°
Step-by-step explanation:
In any regular polygon of n-sided
- All sides are equal in length
- All angles are equal in measure
- The measure of each interior angle is
- The measure of each exterior angle is
- The sum of the measures of the interior and exterior angle at the same vertex is 180°
∵ PQ and QR are two sides of a regular 12-sided polygon
∴ PQ = QR
∵ PR is a diagonal
∴ ∠PQR is an interior angle of the polygon
- By using the rule of the interior angle above
∵ n = 12
∴ m∠PQR =
∴ m∠PQR = 150°
In Δ PQR
∵ PQ = QR ⇒ sides in a regular polygon
- Δ PQR is an isosceles Δ
∴ m∠PRQ = m∠RPQ ⇒ base angles of an isosceles Δ
The sum of the measures of the interior angles of a triangle is 180°
∵ m∠PQR + m∠PRQ + m∠RPQ = 180°
∴ 150 + m∠PRQ + m∠RPQ = 180°
- Subtract 150 from both sides
∴ m∠PRQ + m∠RPQ = 30
∵ m∠PRQ = m∠RPQ
- Divide their sum by 2 to find the measure of each one
∴ m∠PRQ = m∠RPQ = 30 ÷ 2 = 15°
∴ m∠PRQ = 15°
The size of angle PRQ is 15°
Learn more:
You can learn more about the triangles in brainly.com/question/3945600
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