Answer:
The measure of one of the acute angles is 22 degrees, and the measure of the other acute angle is 68 degrees.
Step-by-step explanation:
The angles of a triangle add up to 180 degrees; we know this by the Sum of Angles of a Triangle Theorem.
Then one angle is marked as a right angle meaning it has a measure of 90 degrees.
Using this information and the labels on the diagram we can set up an equation:
x+3x+2+90=180
Now we can solve for x.
4x+92=180
4x=88
x=22 degrees
The measure of one of the acute angles is 22 degrees.
Now to solve for the measure of the other acute angle.
Subsitute the value of x first.
x=22
(3x+2)=?
3*22+2=68 degrees
The measure of the other acute angle is 68 degrees.
A geometric series is the collection of an unlimited number of terms with a fixed ratio between them. The missing value in the table below is 343. The correct option is A.
<h3>What is geometrical series?</h3>
A geometric series is the collection of an unlimited number of terms with a fixed ratio between them.
The given table if closely observed forms a geometric progression, this is because the value of the dependent variable, y is increasing by a common ratio. The common ratio in the table is,
Common ratio = y₂/y₁ = 1/(1/7) = 7
Now, for any geometric progression, the value of the nth term is given as,
Tₙ = a₁ (r)⁽ⁿ⁻¹⁾
where a₁ is the first term of the geometric progression and r is the common ratio. Therefore, the nth term of the series is,
T = a₁ (r)⁽ⁿ⁻¹⁾
Tₙ = (1/7) (7)⁽ⁿ⁻¹⁾
y = (1/7)(7)⁽ˣ⁻¹⁾
Now, the value of the y when the value of x is 5 is,
y = (1/7)(7)⁽ˣ⁻¹⁾
y = (1/7)(7)⁽⁵⁻¹⁾
y = (1/7)(7)⁴
y = (1/7) × 2401
y = 343
Hence, the missing value in the table below is 343.
Learn more about Geometrical Series here:
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The distance between the building and the ladder is 34.876 foot.
<h3>What is a Right Triangle?</h3>
A triangle in which one of the angle measure is equal to 90 degree is called a right triangle.
The ladder forms a right triangle with the building and the ground,
The length of the triangle is 40 foot
The angle made by the ladder is 29.32 degree
By using Trigonometric Ratios
cos 29.32 = Base / Hypotenuse
cos 29.32 = Base / 40
0.8718 × 40 = Base
Base = 34.876 foot
Base is the distance between the building and the ladder.
Base of the ladder = 34.876 foot
To learn more about trigonometric functions from the given link
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Answer:
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Step-by-step explanation:
