Question

What is the answer for question 1 and how

Answer 1

CAB= 180-42= 138/2= 69° as base angles of an isosceles triangle are equal
CAO= 90 as radius meets the tangent at 90°
OAB = 90-68= 21°
AOB= 180-(21+21)
=180-42= 138°
a²= b²+c²-2bcCosA
AB²= 7²+7²-2x7x7Cos138
AB²= 170.8281929
AB= √170.8281929
AB= 13.07012597cm
Or 13.1 to 3sf

Answer 2

Explanation:

ABC is an isoceles triangle (both legs are equally long). and AB is its baseline.

OC is now a median for ABC splitting the angle at C and AB in half.

so, we have 2 right-angled triangles : OAC and OBC.

the half-angles at C are 42/2 = 21°.

the angles at A and B are 90°.

and the half-angles at O are 180 - 90 - 21 = 69°.

remember that the sum of all angles in a triangle must always be 180°.

AB are the heights of both of these triangles.

the single height is sin(69)×7 = 6.535062985... cm

and so,

AB = 2× height = 13.07012597... cm.