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Trigonometry: Area of Triangles

Based on the books answers, **(i) **& **(ii)** are correct but I'm confused about **(ii)**, seeing as how the answer is provided in the question!! Am I meant to prove the statement through the information provided...?

The book's answer to **(iii)** is provided below, but the confusion for me here is the application of tan, in defining the area of the triangle. The 1st attempt in **(iii)** is what I expected the answer to be but, based on the books final answer, I made a second attempt to try and account for tan. Also, again based on the books answer, I'm assuming |ad| is meant to = r but I'm unsure as to how I prove this. Can anyone help me out here?

Many thanks.

Q. A triangle is inscribed in a sector of a circle, center c, radius r, . A right-angled triangle cad circumscribes the sector, as shown. If the area of a sector is , find the area of **(i)** , **(ii)** the sector cab, **(iii)** cad. Hence show that .

**Attempt: (i) **Area of :

|ac| = r = |bc|, where both lines are connected from the center to the circumference of the circle whose sector is cab

Thus, =

**(ii) **

**(iii) **Area of : = = =

**or...?**

=

Ans.: (From text book): (iii)

Re: Trigonometry: Area of Triangles

note that

Re: Trigonometry: Area of Triangles

Thanks.

Ok, so if I'm to demonstrate , and knowing that , I can simply pick any degree from and display the results e.g. in which case = . Although, this leaves me with the problem of the 60 in the middle.

Is there a better way to prove the statement?

Re: Trigonometry: Area of Triangles

Quote:

Originally Posted by

**GrigOrig99** Thanks.

Ok, so if I'm to demonstrate

, and knowing that

, I can simply pick any degree from

and display the results e.g.

in which case

=

. Although, this leaves me with the problem of the 60 in the middle.

Is there a better way to prove the statement?

Re: Trigonometry: Area of Triangles