Answer:
- cos(A) = 3/5
- cos(B) = 0
- cos(C) = 4/5
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relation between the cosine of an angle and the sides of the triangle.
Cos = Adjacent/Hypotenuse
__
<h3>Angle A</h3>
In the given triangle, the hypotenuse is AC. The side adjacent to angle A is AB, so its cosine is ...
cos(A) = AB/AC
cos(A) = 3/5
__
<h3>Angle B</h3>
The right angle in the triangle is angle B. The cosine of a right angle is 0.
cos(B) = 0
__
<h3>Angle C</h3>
The side adjacent to angle C is CB, so its cosine is ...
cos(C) = CB/AC
cos(C) = 4/5
Answer:
23.31 ft
Step-by-step explanation:
Reference angle = 47°
Opp = 25 ft
Adj = x
Apply trigonometry ratio TOA:
Tan 47 = Opp/Adj
Tan 47 = 25/x
x*Tan 47 = 25
x = 25/Tan 47
x = 23.3128772 ≈ 23.31 ft (to 2 d.p)
Answer:
∠PQS= 3(x +5)
Step-by-step explanation:
∠PQR = 5x + 25
∠SQR+∠PQS= 5x+25
∠PQS = ∠PQR-∠SQR
∠PQS= (5x + 25 )-(2x + 10)
∠PQS = 5x+25 -2x-10
∠PQS= 3x +15
∠PQS= 3(x +5)
The geometric sequence is given by:
an=ar^(n-1)
where:
a=first term
r=common ratio
n is the nth term
given that a=4, and second term is -12, then
r=-12/4=-3
hence the formula for this case will be:
an=4(-3)^(n-1)
where n≥1
Answer:
The 13th term is 81<em>x</em> + 59.
Step-by-step explanation:
We are given the arithmetic sequence:
And we want to find the 13th term.
Recall that for an arithmetic sequence, each subsequent term only differ by a common difference <em>d</em>. In other words:
Find the common difference by subtracting the first term from the second:
Distribute:
Combine like terms. Hence:
The common difference is (7<em>x</em> + 5).
To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:
Where <em>a</em> is the initial term and <em>d</em> is the common difference.
The initial term is (-3<em>x</em> - 1) and the common difference is (7<em>x</em> + 5). Hence:
To find the 13th term, let <em>n</em> = 13. Hence:
Simplify:
The 13th term is 81<em>x</em> + 59.
