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give that picture how do I solve for
(h) I know that you you
From the diagram tan(3.5) = h/(13 + x) and tan(9) = h/x. Solve the second equation for x, substitute in the first equation, and solve for h.
i\'m just having a hard time getting a formula for h if you could show me how to do it that would be great...
thanks...
http://mathcentral.uregina.ca/QQ/database/QQ.09.99/angela2.2.gif
ok,first look up tan(3.5)=.061163
so h= (13+x)*tan(3.5)
Then, tan 9 you can look that up
tan9=h/x
or h=x*tan9
setting h=h
(13+x)tan3.5=xtan9
solve for x
Finally, put that into the second equation you typed, and solve for h
h=x*tan9
I would solve each equation for h, and then equate the two right sides ...
form #1
h = (13+x)tan3.5
from #2
h = xtan9
then :
(13+x)tan3.5 = xtan9
13tan3.5 + xtan3.5 = xtan9
13tan3.5 = xtan9 - xtan3.5
13tan3.5 = x(tan9 - tan3.5)
x = 13tan3.5/(tan9 - tan3.5)
evaluate x and sub back into #2
or ...
in the left triangle we can find the other two angles, the one exterior to 9 would be 171, making the top angle 5.5ยบ
Now by the Sine Law you could find the side which is the hypotenuse to the right-angled triangle (call it b)
b/sin3.5 = 13/sin5.5
once you have that hypotenuse the other two sides of the right-angled triangle are easy to find
(Go UofR)
To solve for h using the given diagram, you can follow these steps:
1. Start with the second equation, tan(9) = h/x.
Since we need to solve for h, isolate h by multiplying both sides by x:
x * tan(9) = h
2. Now, substitute this expression for h in the first equation, tan(3.5) = h/(13 + x):
tan(3.5) = (x * tan(9))/(13 + x)
3. Next, cross-multiply to eliminate the fraction:
tan(3.5) * (13 + x) = x * tan(9)
4. Distribute the tan(3.5):
13 * tan(3.5) + x * tan(3.5) = x * tan(9)
5. Rearrange the equation to isolate x terms on one side:
x * tan(3.5) - x * tan(9) = -13 * tan(3.5)
6. Factor out x from both terms:
x * (tan(3.5) - tan(9)) = -13 * tan(3.5)
7. Now, divide both sides by (tan(3.5) - tan(9)):
x = (-13 * tan(3.5))/(tan(3.5) - tan(9))
8. Finally, substitute the value of x back into the second equation to find h:
h = x * tan(9)
After substituting the value of x obtained in step 7 into the equation above, you'll have the formula for h in terms of the given angles and lengths.