ABCD IS a rectangle and line OA is perpendicular to line OB, line BC is equal to 2cm, line CD is equal to 6cm and tan x degree is equal to 3 / 4.find the values of a. sinx b. cos x and c. line OZ.

a) sinx = 3/5

b) cosx = 4/5

c) line OZ = 3cm

Step-by-step explanation:

Two different questions are stated here:

The first is rectangle ABCD where two of its sides are given and we are to find line OZ

The second is on trigonometry. We have been given the tangent ratio and we are to find the sine and cosine ratio.

1) Rectangle ABCD dimensions:

AB = 2cm

CD = 6cm

So we know when we are drawing the rectangle, the smallest side = 2cm and biggest side = 6cm

AO is perpendicular to OB

Line OZ cuts line AB into two

Find attached the diagram

To determine Line OZ, we would apply tangent rule since we know adjacent but opposite is missing.

All 4 angles in a rectangle = 90°

∠OAZ = 45

tan 45 = opposite/adjacent

tan 45 = OZ/3

OZ = 3 × tan45

OZ = 3×1

OZ = 3cm

2) tanx = 3/4

Tangent ratio = opposite/adjacent

opposite = 3, adjacent = 4

see attachment for diagram

Sinx = opposite/hypotenuse

Using Pythagoras theorem

hypotenuse² = opposite² + adjacent²

hypotenuse² = 3²+4² = 9+16 = 25

hypotenuse = √25

hypotenuse = 5

Sinx = opposite/hypotenuse

Sinx = 3/5

Cosx = adjacent/hypotenuse

Cosx = 4/5

a) 3/5

b) 4/5

c) 3cm

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