Answer:
Step-by-step explanation:
<u>Right Triangles</u>
The ratios of the sides of a right triangle are called trigonometric ratios. Each acute angle has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.
The tangent ratio is defined as:
The opposite side is 25 and the adjacent side is 18, thus:
The angle is calculated by using the inverse tangent function:
Answer:
a = 2, r = 5
Step-by-step explanation:
Nth term of a GP = a×r^(n-1)
Where 'a' is the first term and 'r' is the common ratio
4th term = a×r^3 = 250
r^3 = 250/a
7th term = a×r^6 = 31250
a×r^6 = 31250
a×(r^3)^2 = 31250
a×(250/a)^2 = 31250
a×(62500/a^2) = 31250
62500/a = 31250
a = 62500/31250 = 2
a = 2
since r^3 = 250/a,
r^3 = 250/2 = 125
r = (125)^(1/3)
r = 5
This is a proportion question. We can express this as an equation where the answer is
x:
=
From there, you can just cross-multiply and divide to get:
A tenth of 250 is 25, so this is roughly
or
, so it'll be approximately 1.7 inches on the map.
To solve for AC in the given inscribed angle we proceed as follows:
An inscribed angle is an angle with its vertex "on" the circle formed by two intersecting chords as in our drawing. Thus here we shall use the formula:
Inscribed Angle=1/2 intercepted Arc
thus
m∠ABC=1/2mAC
thus plugging in our values we shall have:
4x-3.5=1/2(4x+17)
4x-3.5=2x+8.5
solving simplifying and solving for x we obtain
4x-2x=8.5+3.5
2x=12
hence
x=12/2
x=6°