We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# What on earth is this!?

-1
1009
3 This thing is given by our Math teacher and our "team"(The best 5 students in the grade) does not have any idea how to solve that. But all techniques used are 2 grades lower that our grade...(That is provided by our teacher) :(.

Find x.

Jun 7, 2017
edited by MaxWong  Jun 7, 2017
edited by MaxWong  Jun 7, 2017
edited by MaxWong  Jun 7, 2017

### Best Answer

#2
+3

Here's one approach:

Without loss of generality let AB = 1

Angle ADB = 180-80-50 = 50 so triangle ABD is isosceles and AD = AB = 1

Angle AEB = 180-60-80 = 40,  so AE/sin(80) = 1/sin(40) or AE = sin(80)/sin(40)

Angle BDE = 180-30-(40+x) = 110-x

Angle ADE = ADB + BDE = 50 + 110 - x = 160 - x

Sine rule on triangle ADE:

sin(x)/AD = sin(160-x)/AE or sin(x)/1 = sin(160-x)*sin(40)/sin(80)

Rearrange:  sin(80)*sin(x) = sin(40)*sin(160-x)

sin(80)*sin(x) = sin(40)*(sin(160)*cos(x) - cos(160)*sin(x))

I'm sure you can take it from here (collect sin(x) terms on one side, cos(x) on the other, divide to get tan( x) ...etc.)

As Guest #1 notes, you should find x = 30 degrees.

.

Jun 7, 2017
edited by Alan  Jun 7, 2017

### 3+0 Answers

#1
0

hectictar: You can do this!. Hint: angle AEB=40 degrees, and x=30 degrees !!.

Jun 7, 2017
#2
+3
Best Answer

Here's one approach:

Without loss of generality let AB = 1

Angle ADB = 180-80-50 = 50 so triangle ABD is isosceles and AD = AB = 1

Angle AEB = 180-60-80 = 40,  so AE/sin(80) = 1/sin(40) or AE = sin(80)/sin(40)

Angle BDE = 180-30-(40+x) = 110-x

Angle ADE = ADB + BDE = 50 + 110 - x = 160 - x

Sine rule on triangle ADE:

sin(x)/AD = sin(160-x)/AE or sin(x)/1 = sin(160-x)*sin(40)/sin(80)

Rearrange:  sin(80)*sin(x) = sin(40)*sin(160-x)

sin(80)*sin(x) = sin(40)*(sin(160)*cos(x) - cos(160)*sin(x))

I'm sure you can take it from here (collect sin(x) terms on one side, cos(x) on the other, divide to get tan( x) ...etc.)

As Guest #1 notes, you should find x = 30 degrees.

.

Alan Jun 7, 2017
edited by Alan  Jun 7, 2017
#3
0

yo tengo una preg pata ti haber sie eres inteligente

dos angulos coeterminales estan en relacion de 11a 3 halla el valor del menor de eellos si  el mayor se encuentra en el intervalo de 450 a500

Jun 11, 2017