Question

The ratio of the base of an isosceles triangle to its altitude is 43.85:4. Find the measure of one of the congruent angles (in radians) of the triangle. Round off your answer to two decimal places.

Answer 1

can someone help me please? my answe is 31.05 but got a wrong answer

Answer 2

tan ø = 4 / (43.85/2)

ie tan is height over half-base

draw it and see.

it's a small angle so i'd use tan ø = ø and leave it there.

Answer 3

i got an anwer of 10.33 degrees and in radians 0.180 rad

Answer 4

@IrishBoy123 am I on the right path?

Answer 5

yep!! well done.

Answer 6

@IrishBoy123 mind if I ask 2 more questions?

Answer 7

sure

Answer 8

I really need to ace this one I only got 120/150 by now, 3 questions are in the way...

Answer 9

Determine the area of the segment of a circle if the length of the chord is 15 inches and located 4.14 inches from the center of the circle. Round off your answer to two decimal places. (Thank you so much for the help)

Answer 10

is that right?

Answer 11

Yep!!! exactly

Answer 12

ok! Now please keep in mind that the area A of the triangle AOB is given by the subsequent formula:
\[A = \frac{{AB \times OH}}{2}\]
so, what is A?

Answer 13

hint:
\[AB = 15,\quad OH = 4.14\]

Answer 14

hint:
what is:
\[A = \frac{{15 \times 4.14}}{2} = ...?\]

Answer 15

31.05 - exact anser I had when I submitted it and got an incoorrect answer @Michele_Laino

Answer 16

please note that that's the area of the triangle, not the area of the circular segment

Answer 17

now, you have to find the area S of the circular sector

Answer 18

that area S is given by the subsequent formula:
\[S = \frac{{ arc(AB)\times r}}{2}\]
where r is the radius of our circumference, and:
arc(AB) is the length of the arc AB

Answer 19

plase note that I can compute the area S using the subequent formula:
\[S = \frac{{{r^2}}}{2}\sin \alpha \]

Answer 20

@Michele_Laino ahh ok so I derived a formula for finding the area of the segmen = 1/2 r^2(Theta - sin theta) (is it correct?

Answer 21

ok!

Answer 22

hint:
\[{r^2} = {7.5^2} + {4.15^2} = ...?\]

Answer 23

please wait, I'm gong to check your result...

Answer 24

I got 0.58

Answer 25

I got this:
\[\sin \theta = \frac{{2S}}{{{r^2}}} = \frac{{2 \cdot 31.05}}{{73.38}} = \frac{{62.1}}{{73.38}} = 0.8462\]

Answer 26

so:
\[\theta = 1.009\;radians\]