Question 86 – 3.5 Trigonometry (A-level only) - Questions

A design for a decorative stained-glass window panel is shown below. The design consists of a sector $OBC\,$ of a circle with centre $O$ , flanked by two congruent triangles $OAB\,$ and $O D C$ . The point $O\,$ lies on the straight base $A D$ . The points $B\,$ and $C\,$ lie on the arc of the circle. The side lengths $AB\,$ and $DC\,$ are equal, and the angles $\angle AOB\,$ and $\angle DOC\,$ are equal and acute.

Given that:

angle $B O C = 1.8$ radians
area of sector $\text{ cm}^2$
$AOD\,$ is a straight line of length 15.0 cm

Find the radius of the sector, giving your answer in $cm\text{cm}$ to 2 decimal places.

Find the size of angle $A O B$ , in radians, to 2 decimal places.

Hence find: the total area of the window panel, giving your answer in $cm2\text{cm}^2$ to one decimal place.

the total perimeter of the panel, giving your answer in $cm\text{cm}$ to one decimal place.

Given that:

angle $B O C = 1.8$ radians
area of sector $\text{ cm}^2$
$AOD\,$ is a straight line of length 15.0 cm

Find the radius of the sector, giving your answer in $cm\text{cm}$ to 2 decimal places.

Find the size of angle $A O B$ , in radians, to 2 decimal places.

Hence find: the total area of the window panel, giving your answer in $cm2\text{cm}^2$ to one decimal place.

the total perimeter of the panel, giving your answer in $cm\text{cm}$ to one decimal place.

3.5 Trigonometry (A-level only)

Question 73

3.5 Trigonometry (A-level only)

Question 73

3.5 Trigonometry (A-level only)

Question 73

3.5 Trigonometry (A-level only) Questions

3.5 Trigonometry (A-level only)

Question 73

3.5 Trigonometry (A-level only) Questions