Engineering Mechanics - General Principles - Discussion

Guys here we can't use trigonometry relations.

Because one of them angle is not 90°.

I totally agree with you @Devendra, by using sin formula one can solve this problem in an accurate manner.

In triangle ABC, angle A is given 40, By applying the formula.

6/sin 40 = 7/sin B, we get sin B = 48.58.

Now the sum of all angles of triangle = 180.

We get angle C = 91.4.

Again 6/sin 40 = c/sin 91. 4, we get C = 9.33.

We can not use trigonometry or Pythagoras theorem unless we have right angle triangle, here the figure is seems to be right angle triangle but it is not.

So we can use sin formula a/sinA=b/sinB=c/sinC where a, b, c are the sides opposites to the angle A, B, C.

bc = 6, ac = 7 ab = ? now, trigonometric from ab^2 = bc^2+ac^2.

ab^2 = 36+49 = 9.21.

Answer = D.

I think 1st we check about diagonal ,so according to pythagorean triangle formula. 6*2+7*2=h*2( * means power ) so h =9.22 , but if angle angle acb is 90. So then see the option, in option A and option D h=9.22, but in that 2 option angle acb not 90 degree.

Then in option C angle is 90 degree but diagonal h is not 9.22, so this is also incorrect. Because if angle is 90 then h must be 9.22.

So easily you without calculation you may find option D is. correct.... thanks.

Need to apply sin rule,
AB/sin(C) = BC/sin(A) = CA/sin(B)

IN THE PROBLEM,
AC=7, BC=6 AND ANGLE A=40 GIVEN

AB/sin(C) = 6/sin(40) = 7/sin(B).
sin(B) = [7*sin(40)]/6 from this we will get B angle.

Then C=180-A-B.
AFTER THAT AB = [6/sin(40)]*sin(C).

Why cant we use cos40=7/AB=>AB=9.14 directly......it is also correct method.

See you are right but sin(theta) is also used for side and angle relation.

Like formula is a/sin(alpha)=b/sin(bita)=c/sin(gama).
Where a,b,c are the sides of triangle and alpha, bita,gama are the angle infront of side of triangle like a, b, c.

So we can solve as:
7/sin(fai)=6/sin(40)
so sin(fai)=0.7499
and fai=48.58 degree.

Also theta=180-(40+48.58)=91.42 degree.

And using same formula as above we can find length AB as

6/sin(40)=AB/sin(91.42)

so AB=9.33

COS40=7/AB
AB=7/COS40
AB=9.13

Please let me know why you are using Sin theta, I think sin is using against for length / hypotenus, we get for cos theta also because we know base of triangle. Then answer is 9.22.