How to apply the cosine rule here?
up vote
-4
down vote
favorite
ABC is an equilateral triangle. D is a point on BC and AD is produced to E such that $angle EAC= angle EBC.$ Find the length of AE given that BE=5 and CE= 12
trigonometry
edited Nov 14 at 15:10
Dhamnekar Winod
358414
asked Nov 14 at 14:37
Shivansh J
126
add a comment |
up vote
-4
down vote
favorite
ABC is an equilateral triangle. D is a point on BC and AD is produced to E such that $angle EAC= angle EBC.$ Find the length of AE given that BE=5 and CE= 12
trigonometry
edited Nov 14 at 15:10
Dhamnekar Winod
358414
asked Nov 14 at 14:37
Shivansh J
126
1
Its equilateral!
– QuIcKmAtHs
Nov 14 at 14:38
Hint. Observe that $E$ must lie on the circumcircle of $Delta ABC$, which would mean $angle BEC = frac{2pi}{3}$.
– Faustus
Nov 14 at 14:50
Yes, you are right but I have no idea about how to use this
– Shivansh J
Nov 14 at 14:52
@ShivanshJ I got the answer i-e the length of AE=17. But i used triangle calculator.Cosine rule is $a=sqrt{b^2+c^2-2*b*c*cos{A}}$
– Dhamnekar Winod
Nov 14 at 17:21
@ShivanshJ,you must use sine rule as well.
– Dhamnekar Winod
Nov 15 at 4:01
add a comment |
up vote
-4
down vote
favorite
up vote
-4
down vote
favorite
ABC is an equilateral triangle. D is a point on BC and AD is produced to E such that $angle EAC= angle EBC.$ Find the length of AE given that BE=5 and CE= 12
trigonometry
edited Nov 14 at 15:10
Dhamnekar Winod
358414
asked Nov 14 at 14:37
Shivansh J
126
ABC is an equilateral triangle. D is a point on BC and AD is produced to E such that $angle EAC= angle EBC.$ Find the length of AE given that BE=5 and CE= 12
trigonometry
trigonometry
edited Nov 14 at 15:10
Dhamnekar Winod
358414
asked Nov 14 at 14:37
Shivansh J
126
edited Nov 14 at 15:10
Dhamnekar Winod
358414
asked Nov 14 at 14:37
Shivansh J
126
edited Nov 14 at 15:10
Dhamnekar Winod
358414
edited Nov 14 at 15:10
Dhamnekar Winod
358414
edited Nov 14 at 15:10
Dhamnekar Winod
358414
358414
asked Nov 14 at 14:37
Shivansh J
126
asked Nov 14 at 14:37
Shivansh J
126
asked Nov 14 at 14:37
Shivansh J
126
126
1
Its equilateral!
– QuIcKmAtHs
Nov 14 at 14:38
Hint. Observe that $E$ must lie on the circumcircle of $Delta ABC$, which would mean $angle BEC = frac{2pi}{3}$.
– Faustus
Nov 14 at 14:50
Yes, you are right but I have no idea about how to use this
– Shivansh J
Nov 14 at 14:52
@ShivanshJ I got the answer i-e the length of AE=17. But i used triangle calculator.Cosine rule is $a=sqrt{b^2+c^2-2*b*c*cos{A}}$
– Dhamnekar Winod
Nov 14 at 17:21
@ShivanshJ,you must use sine rule as well.
– Dhamnekar Winod
Nov 15 at 4:01
add a comment |
1
Its equilateral!
– QuIcKmAtHs
Nov 14 at 14:38
Hint. Observe that $E$ must lie on the circumcircle of $Delta ABC$, which would mean $angle BEC = frac{2pi}{3}$.
– Faustus
Nov 14 at 14:50
Yes, you are right but I have no idea about how to use this
– Shivansh J
Nov 14 at 14:52
@ShivanshJ I got the answer i-e the length of AE=17. But i used triangle calculator.Cosine rule is $a=sqrt{b^2+c^2-2*b*c*cos{A}}$
– Dhamnekar Winod
Nov 14 at 17:21
@ShivanshJ,you must use sine rule as well.
– Dhamnekar Winod
Nov 15 at 4:01
1
1
Its equilateral!
– QuIcKmAtHs
Nov 14 at 14:38
Its equilateral!
– QuIcKmAtHs
Nov 14 at 14:38
Hint. Observe that $E$ must lie on the circumcircle of $Delta ABC$, which would mean $angle BEC = frac{2pi}{3}$.
– Faustus
Nov 14 at 14:50
Hint. Observe that $E$ must lie on the circumcircle of $Delta ABC$, which would mean $angle BEC = frac{2pi}{3}$.
– Faustus
Nov 14 at 14:50
Yes, you are right but I have no idea about how to use this
– Shivansh J
Nov 14 at 14:52
Yes, you are right but I have no idea about how to use this
– Shivansh J
Nov 14 at 14:52
@ShivanshJ I got the answer i-e the length of AE=17. But i used triangle calculator.Cosine rule is $a=sqrt{b^2+c^2-2*b*c*cos{A}}$
– Dhamnekar Winod
Nov 14 at 17:21
@ShivanshJ I got the answer i-e the length of AE=17. But i used triangle calculator.Cosine rule is $a=sqrt{b^2+c^2-2*b*c*cos{A}}$
– Dhamnekar Winod
Nov 14 at 17:21
@ShivanshJ,you must use sine rule as well.
– Dhamnekar Winod
Nov 15 at 4:01
@ShivanshJ,you must use sine rule as well.
– Dhamnekar Winod
Nov 15 at 4:01
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
draft saved
draft discarded
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2998328%2fhow-to-apply-the-cosine-rule-here%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
Its equilateral!
– QuIcKmAtHs
Nov 14 at 14:38
Hint. Observe that $E$ must lie on the circumcircle of $Delta ABC$, which would mean $angle BEC = frac{2pi}{3}$.
– Faustus
Nov 14 at 14:50
Yes, you are right but I have no idea about how to use this
– Shivansh J
Nov 14 at 14:52
@ShivanshJ I got the answer i-e the length of AE=17. But i used triangle calculator.Cosine rule is $a=sqrt{b^2+c^2-2*b*c*cos{A}}$
– Dhamnekar Winod
Nov 14 at 17:21
@ShivanshJ,you must use sine rule as well.
– Dhamnekar Winod
Nov 15 at 4:01