Set up a right triangle model for this problem and solve by using the reference table trigonometric ratio that applies. follow the models above.
a photographer stands 60 yards from the base of a lighthouse and observes that the angle between the ground and the top of the lighthouse is 41°. how tall is the lighthouse?
a.45.3 yards
b.52.2 yards
c.39.4 yards

B. 52.2 yards

Lighthouse is 52.2 yards tall.

Step-by-step explanation:

Let AB denotes the height of the lighthouse & BC denotes the distance between the base of a lighthouse and Photographer.

In Figure,  ∠ACB = 41° & ∠ABC = 90°, Threrefore,  Base is BC and perpendicular is AB.

As we know, tan(∠ACB) =

∴  tan 41° =

tan 41° =

0.869286737 =

AB = 52.2 yards ( approx.)

Thus, Height of the lighthouse is 52.2 yards

more detail

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form