Given: △abc, ab=5 sqrt2 m∠a=45°, m∠c=30° find: bc and ac
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The measure of side BC = 5 unit and The measure of side AC = 5 unit

Step-by-step explanation:

Given as :

In a triangle ΔABC

The measure of side = AB = 5 unit

The measure of angle A = ∠A = 45°

The measure of angle C = ∠C = 30°

Now, For a triangle the sum of three angles of triangle = 180°

∴, ∠A + ∠B + ∠C = 180°

Or, 45° + ∠B +30° = 180°

Or , ∠B =  180° - ( 45° +  30°)

Or,  ∠B =  180° - 75°

i.e  ∠B =  105°

Now, From figure

Sin 45°  =

Or, =

Or, BC =

∴ BC = 5

So, The measure of side BC = 5 unit

Again , from figure

Cos 45°  =

Or, =

Or, AC =

∴  AC = 5

So, The measure of side AC = 5 unit

Hence The measure of side BC = 5 unit and The measure of side AC = 5 unit  Answer

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

*calories burned = (weight)(calorie factor)*

calories burned = 180 (0.65)

calories burned = 117

the calories he used up is 117, which is 65% of his weight.