Solve the right triangle ABC with right angle C, if B=30 degrees, and C = 10
1 answer:
Answer:
The answer to your question is letter D
Step-by-step explanation:
We know that the sum of the internal angles in a triangle equals 180°.
So, B = 30°, C = 90° and A = ?
A + B + C = 180°
Substitution
A + 30 + 90 = 180
Solve for A
A = 180 - 30 - 90
A = 180 - 120
A = 60°
To find "b". use the trigonometric function sine
sin B =
sin B x hypotenuse = Opposite side
Opposite side = sin 30 x 10
Opposite side = 0.5 x 10
Opposite side = b = 5.0
To find "a" use the trigonometric function cosine
Cos A = adjacent side / hypotenuse
Adjacent side = a = cos A x hypotenuse
Adjacent side = a = cos 60 x 10
a = 0.866 x 10
a = 8.66
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54 
A right triangle is a shape that looks like half of a square. The height of the triangle is 12, and the base of the triangle is 9. To find the area, use the following formula:
A =
=
=
= 54
A right triangle is a shape that looks like half of a square. The height of the triangle is 12, and the base of the triangle is 9. To find the area, use the following formula:
A =
=
=
= 54
Answer:
740
Step-by-step explanation:
The n th term of an arithmetic series is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = 7 and a₇ = (3 × 7) + 2 = 21 + 2 = 23 , then
a₁ + 2d = 7 → (1)
a₁ + 6d = 23 → (2)
Subtract (1) from (2) term by term
4d = 16 ( divide both sides by 4 )
d = 4
Substitute d = 4 into (1)
a₁ + 2(4) = 7
a₁ + 8 = 7 ( subtract 8 from both sides )
a₁ = - 1
The sum to n terms of an arithmetic series is
=
[ 2a₁ + (n - 1)d ] , thus
=
[ (2 × - 1) + (19 × 4) ]
= 10(- 2 + 76) = 10 × 74 = 740