Find the area of a triangle when a=22 degree, b=105 degree, and b=14 30.4 units^2 32.1 units^2 31.2 units^2 34.8 units^2

Option A. 30.4 unit²

Step-by-step explanation:

In the given triangle ABC, side AC = 14 units, ∠ BAC = 22° and ∠ ABC = 105°.

We have to find the area of ΔABC.

Since area of an obtuse triangle =

Here Base = x

Height = h

To find the measure of Base "x".

We will apply the sine rule in ΔABC

We cross multiply on both the sides

14×0.375 = 0.966×(x)

5.25 = 0.966x

x =

x = 5.43 unit

For the measurement of Height "h"

h = 0.978×14 = 11.18 unit

Now we put the values of base and height in the formula

Area of Δ ABC =

                        =

                        = 30.35 ≈ 30.4 unit²

4sqrt5

step-by-step explanation:

the base has dimensions of 8 x 4, so the diagonal is 64 + 16 square rooted or 4sqrt5.

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°